3 edition of **Elliptic equations in polyhedral domains** found in the catalog.

Elliptic equations in polyhedral domains

V. G. MazК№iпё aпёЎ

- 291 Want to read
- 36 Currently reading

Published
**2010** by American Mathematical Society in Providence, R.I .

Written in English

- Differential equations, Elliptic,
- Polyhedra -- Models,
- Boundary value problems

**Edition Notes**

Includes bibliographical references and index.

Statement | Vladimir Maz"ya, Jurgen Rossmann. |

Series | Mathematical surveys and monographs -- v. 162 |

Contributions | Rossmann, J. 1954- |

Classifications | |
---|---|

LC Classifications | QA377 .M296 2010 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL24013628M |

ISBN 10 | 9780821849835 |

LC Control Number | 2009053203 |

OCLC/WorldCa | 499129712 |

V. A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc., 16 (), Google Scholar [13] V. A. Kondart'ev and O. A. Oleinik, Boundary value problems for partial differential equations in nonsmooth domains, Russian :// Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones Stephan Dahlke Philipps Universität Marburg non-elliptic equations [5], saddle point problems [11] and also nonlinear operator equations wavelet schemes for problems in polyhedral domains is also justi :// Abstract. This paper is dedicated to the memory of Professor Søren Jensen Numerical methods for computing singular solutions of linear second order elliptic partial differential equations (Laplace and Elasticity problems) in polyhedral domains are ://

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The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points.

The book is destined for graduate students and researchers working in elliptic partial differential equations and :// ISBN: OCLC Number: Description: vii, pages: illustrations ; 27 cm. Contents: pt. The Dirichlet problem for strongly elliptic systems in polyhedral domains Neumann and mixed Elliptic equations in polyhedral domains book value problems for second order systems in polyhedral domains --pt.

boundary value problems for stationary stokes and Navier-Stokes systems in polyhedral Elliptic Equations in Polyhedral Domains Maz ′ ya and Rossmann Elliptic Equations in Polyhedral Domains Vladimir Maz′ya Jürgen Rossmann 4-color Process / Pantone ProcessPantone Process Pantone Process SURV/ This is the first monograph which systemati-cally treats elliptic boundary value problems in domains of Genre/Form: Electronic books: Additional Physical Format: Print version: Mazʹi︠a︡, V.G.

Elliptic equations in polyhedral domains book equations in polyhedral domains. Providence, R.I.: American Buy Elliptic Equations in Polyhedral Domains (Mathematical Surveys and Monographs) on FREE SHIPPING on qualified orders The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points.

The book is destined Elliptic equations in polyhedral domains book graduate students and researchers working in elliptic partial differential equations and :// solutions to the Dirichlet problem for quasilinear elliptic equations Elliptic equations in polyhedral domains book domains with smooth closed edges of arbitrary dimension.

Chapters 3 and Elliptic equations in polyhedral domains book (Dirichlet problem in domains of polyhedral type). Pointwise estimates for Green’s matrix of the Dirichlet problem for strongly elliptic equations of higher order were obtained in our paper [] Elliptic Equations in Polyhedral Domains About this Title.

Vladimir Maz′ya, Linköping University, Linköping, Sweden and Jürgen Rossmann, Rostock University, Rostock, Germany. Publication: Mathematical Surveys and Monographs Publication Year Volume ISBNs: (print); (online) Elliptic problems on polyhedral domains We now proceed to study solution to elliptic boundary value problems on polygonal and polyhedral domains.

Our goal is to gain a thorough understanding of singularity structure and regularity of Poisson’s problem in such domains. Much of what we learn about the Laplacian can be extended~demlow/Courses/16_sp/_sp16/hw_sol/ second order elliptic systems in polyhedral domains by V.

Mazya and J. Rossmann Abstract Boundary value problems for second order elliptic diﬁerential equations and systems in a polyhe-dral domain are considered. The authors prove Schauder estimates and obtain regularity assertions for This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains.

These are presented in an engineering terminology for practical :// equations The Dirichlet problem for the biharmonic equation in an angle The Dirichlet problem for the biharmonic equation in a cone The polyharmonic operator The Dirichlet problem for A2 in domains with piecewise smooth boundaries Notes Part 2.

Singularities of solutions to general elliptic Singular quasilinear elliptic systems and Hölder regularity Giacomoni, Jacques, Schindler, Ian, and Takáč, Peter, Advances in Differential Equations, On the existence and nonexistence of solutions for an elliptic system in unbounded domains Sato, Jun-ichi, Advances in Differential Equations, Nečas’ book Direct Methods in the Theory of Elliptic Equations, published in French, Elliptic equations in polyhedral domains book become a standard reference for the mathematical theory of linear elliptic equations and systems.

This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in /second-order-elliptic-equations-and-elliptic-systems. Anisotropic graded meshes and quasi-optimal rates of convergence for the FEM on polyhedral domains in 3D.

ECCOMAS - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers, Elliptic Problems for Pseudo Differential Equations in a Polyhedral Cone Vladimir B. Vasilyev Lipetsk State Technical University Chair of Pure Mathematics Lipetsk,Russia [email protected] Abstract The author develops the theory of pseudo differential equations and boundary value problems in nonsmooth Numerical methods for computing singular solutions of linear second order elliptic partial differential equations (Laplace and Elasticity problems) in polyhedral domains are presented.

The singularities may be caused by edges, vertices, or abrupt changes in material properties or boundary conditions. In the vicinity of the singular lines or~yosibash/papers/ANM_pdf.

We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\partial\Omega$ such as, e.g., boundaries of polyhedral domains $\Omega \subset \mathbb{R}^3$. New elliptic regularity results for polyhedral Laplace interface problems for anisotropic materials are established by V.

Maz’ya, J. Elschner, J. Rehberg and G. Schmidt [], Some unilateral boundary value problems (e.g., Signorini transmission problems with mixed boundary conditions) in polygonal and polyhedral domains are studied in [82].

“The book is devoted to substantial and systematic presentation of the linear and nonlinear theory of elliptic partial differential equations in unbounded domains. The presentation of › Birkhäuser › Mathematics.

Our curved polyhedral domains are allowed to have cracks. We establish a well-posedness result when there are no neighboring traction boundary conditions and |a| 0 that depends on P, on the boundary conditions, and on the domain Ω. Our results extend to other strongly elliptic systems and higher :// Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects.

This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic :// Besov regularity of edge singularities for the Poisson equation in polyhedral domains Article in Numerical Linear Algebra with Applications 9(6‐7) - September with 2 Reads Elliptic equations in polyhedral domains Vladimir Maz'ya, Jürgen Rossmann （Mathematical surveys and monographs, v.

） American Mathematical Society, It is well known that in the case of a regular domain the solution of the time-harmonic Maxwell's equations allows a discretization by means of nodal finite elements: this is achieved by solving a regularized problem similar to the vector Helmholtz equation.

The present paper deals with the same problem in the case of a nonconvex :// we mainly restrict ourselves to the situation of homogeneous elliptic equations with constant coefﬁcients.

Generalizations to operators with lower orde r terms and variable coefﬁcients will be brieﬂy indicated. They will be discussed in more deta il in our forthcoming book [16]. Organization of In this review, we aim to introduce Pohozaev identity and its applications in some classical elliptic partial differential equations.

First, we introduce Pohozaev identities for several typical elliptic equations on bounded domains or unbounded domains, and the necessary conditions for the existence of solutions, by which we get some existence and nonexistence results of the A classic text focusing on elliptic boundary value problems in domains with nonsmooth boundaries and problems with mixed boundary conditions.

This book is for researchers and graduate students in computational science and numerical analysis who work with theoretical and numerical PDEs. Accessible to those with a background in functional › Books › Science & Math › Mathematics.

This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and › Mathematics › Analysis.On finite element methods for elliptic equations on domains with corners.

Computing 28 () 53 – [12] Băcuţă, C., Nistor, V. and Zikatanov, L.T., Improving the rate of convergence of high-order finite elements in polyhedra II: mesh refinements and :// Effect of the boundary conditions in the behavior of the optimal constant of some Caffarelli-Kohn-Nirenberg inequalities.

Application to some doubly critical nonlinear elliptic problems Abdellaoui, B., Colorado, E., and Peral, I., Advances in Differential Equations, ; Regularity for solutions to nonlinear elliptic equations Greco, Luigi, Moscariello, Gioconda, and Zecca, Gabriella SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () C 1 quintic splines on domains enclosed by piecewise conics and numerical solution of fully nonlinear elliptic :// ANISOTROPIC REGULARITY AND OPTIMAL RATES OF CONVERGENCE FOR THE FINITE ELEMENT METHOD ON THREE DIMENSIONAL POLYHEDRAL DOMAINS CONSTANTIN BACUT˘ A, ANNA L.

MAZZUCATO, AND VICTOR NISTOR Abstract. We consider the model Poisson problem u = f 2, u = g on @, where is a bounded polyhedral domain in Rn. The objective of the paper Elliptic problems on polyhedral domains, TAMU.

Grisvard, P.: Elliptic problems in non-smooth domains. London: Pitman Karl Gustafson and Takehisa Abe. The third boundary condition—was it robin’s.

The Mathematical Intelligencer, MarchVol Issue 1, pp Assume from now on that Ω is a domain with a polyhedral structure and let ϑ(x) denote the distance from xto the edges of Ω. (The “domains with a polyhedral structure” are a generalization of the polyhedral domains [27] and allow for cracks.

Their deﬁnition is recalled in Section 3.) We shall always take f = ϑ,orsome regularization of ~ Elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks Anna L.

Mazzucato, Victor Nistor nomenon of loss of regularity for elliptic problems on non-smooth domains, a phenomenon extensively discussed in many research papers, including [29, The book by Kozlov, Mazya, and Rossmann [53] is a good elliptic scalar equation.

We deﬁne curvilinear polyhedral domains inductively in Section 2. We allow polyhedral domains to be disconnected for technical rea-sons, more precisely, for the purpose of deﬁning them inductively.

Our results, however, are formulated for connected polyhedral domains. Many polyhedral Documenta Mathematica 15 ( In this paper, we study the regularity of the solutions of some nonlinear elliptic equations in Kondratiev spaces on certain domains of polyhedral type.

General embedding theorems between Kondratiev spaces and Besov spaces will allow to avoid drawbacks to the standard Sobolev regularity theory for those nonsmooth :// SOBOLEV SPACES 3 ﬁrst that Km a(Ω) is isomorphic to a Sobolev space on a certain non-compact Rie- mannian manifold M with smooth boundary.

This non-compact manifold M is obtained from our polyhedral domain by replacing the Euclidean metric gE with (4) r−2 P gE, rP a smoothing of ϑ, which blows up at the faces of codimension two or higher, that is, at the set elliptic scalar equation.

We de ne curvilinear polyhedral domains inductively in Section 2. We allow polyhedral domains to be disconnected for technical rea-sons, more precisely, for the purpose of de ning them inductively.

Our results, however, are formulated for connected polyhedral domains. Many polyhedral Documenta Mathematica 15 () {~bacuta/papers/.

Pdf - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper is dedicated to the memory pdf Professor Søren Jensen Numerical methods for computing singular solutions of linear second order elliptic partial differential equations (Laplace and Elasticity problems) in polyhedral domains are presented.

The singularities may be caused by edges, vertices, or abrupt changes ?doi= A brief history of elliptic BVP with corners: Russian school V.

Download pdf. KONDRAT’EV Boundary-value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16 ()– 1 Domains with conical points 2 Scalar elliptic BVP 3 Hilbert Sobolev spaces with or without weights 4 Fredholm, regularity 1 Ebook and mixed boundary value problems on n-dimensional polyhedral domains Constantin B acut˘ a1, Anna L Mazzucato2, Victor Nistor3, and Ludmil Zikatanov4 Abstract.

Let 2Z + be arbitrary. We prove a well-posedness result for mixed boundary