Strongly elliptic systems and boundary integral equations

By M. Mudge. Mathematical Gazette, 2000

2,806 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c16450b40568f6a9cb57b5aa65a19966ce588705

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains (2011, background): “be the strong (classical) modified co-normal derivative (it corresponds to B̃ν v in [13]), associated with the operator A∗ .”
On the Mathematical Basis of the Linear Sampling Method (2003, background): “[8]), and w has the asymptotic behavior (1.”
Analysis of FRP–concrete debonding via boundary integral equations (2008, methodology): “As a main consequence of this variational framework, Galerkin approximation scheme [41] can be adopted.”
AN APPROXIMATION PROPERTY OF IMPORTANCE IN INVERSE SCATTERING THEORY (2001, background): “2 now yield our desired approximation result, where in the theorem the normal derivative of u is in H−1/2(∂D), since u ∈ H1(D) is a solution of the Helmholtz equation [7].”
Non-self-adjoint operators, infinite determinants, and some applications (2005, background): “Since it follows from the first Green’s formula (cf., e.g., [ 33, Theorem 4.4 ]) that HD”
Approximation capability of a bilinear immersed finite element space (2008, background): “We note that (H5) will hold if is sufficiently smooth, see the results of [74, 75] on the transmission problems.”
Integral equations for inverse problems in corrosion detection from partial Cauchy data (2007, methodology): “1) then we obtain an H(1)(D) solution of the Laplace equation [18].”
Sobolev Spaces on Non-Lipschitz Subsets of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^n$$\end{doc (2016, positive): “28 in [38], which is the most restrictive of this list as it considers only sets with bounded boundaries for which sets it is equivalent to the “uniform cone condition” [23, Theorem 1.”
Quantitative Runge Approximation and Inverse Problems (2017, background): “d ponly depend on Ω, n, and M. Proof. The last statement follows from [Mey63, Theorem 1] (Lipschitz domains are admissible by [JK95, Theorem 0.5]). The other statements are standard (see for instance [McL00]). We will next prove Theorem 1. Deﬁne the space He1/2(Γ) = closure of {g∈ H1/2(∂D 2); supp(g”
Mixed Finite Elements, Compatibility Conditions, and Applications (2008, background): “We also refer the reader to [32, 31], where general results were obtained, and to the books [17, 45, 37].”
Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains (2014, neutral): “[33, 43].”
On Invertibility of Elastic Single-Layer Potential Operator (2004, background): “Single-layer Potential Solution of the Dirichlet Problem Let us consider an elastic body defined by an open and connected set, a domain, ⊂ R2 with a bounded Lipschitz boundary [25] ∂ = (i.”