Dirichlet problems on varying domains

101 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, background): “The main source for these results is [58].”
A Faber-Krahn inequality for Robin problems in any space dimension (2006, unknown): “the same volume as � n. Then, by the above result λ1(Bn) ≤ λ1(� n) for all n ∈ N. Then λ1(Bn) → λ1(B) and λ1(� n) → λ1(�) (see for instance [ 11, Section 4 ]).”
Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains (2010, unknown): “, [4, 15] for the case of bounded domains).”
Geometrical Structure of Laplacian Eigenfunctions (2012, background): “the space of eigenfunctions in the limiting (disconnected) domain Ω is the direct product of spaces of eigenfunctions for each subdomain Ωi (see [112] for discussion on convergence and related issues).”
Maximum Principles and Principal Eigenvalues (2005, background): “Of course, in the case of Dirichlet boundary conditions for a scalar equation much more general results can be obtained as has been shown by Daners [28], [29] and others (see the remarks following Theorem 18).”