Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations

By Daniel B. Henry, Jack K. Hale, Antonio L Pereira. 2005

216 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/05791a1d7c2366cbf6a0e023537218541ab3425e

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

A few shape optimization results for a biharmonic Steklov problem (2015, methodology): “We refer to [27] for a general approach to domain perturbation problems (see also [25]), and to [26] for a comprehensive discussion on eigenvalue shape optimization problems for elliptic operators.”
Spectral stability of Dirichlet second order uniformly elliptic operators (2008, background): “, Hale [11], Henry [12], Lamberti and Lanza de Cristoforis [16], Sokolowsky and Zolésio [23] and the references therein.”
Eigenvalues of poly-harmonic operators on variable domains (2012, methodology): “For r = 1, n = 1, m = 0 or n = 2, m = 0 this can be proved by using the celebrated moving plane method under the assumption that the solution u1 does not change sign (see e.g., Henry [14] for the Laplace operator and Dalmasso [8] for the biharmonic operator); for r = 1, n = 2, m = 1 a different meth”
Geometrical Structure of Laplacian Eigenfunctions (2012, background): “The spectral stability of elliptic operators under domain perturbations has been thoroughly investigated [105, 106, 107, 108, 109, 226, 240].”
Dynamics in dumbbell domains I. Continuity of the set of equilibria (2006, background): “See also [16] for a survey on results on the behavior of eigenvalues under perturbations of the domain and [21] for a general method to treat regular perturbations of the domain.”
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, unknown): “For the theory of smooth perturbations rather complementary to ours we refer to [84] and references therein.”