Partial Differential Equations of Elliptic Type

By Allaberen Ashyralyev, P. Sobolevskiĭ. 2004

321 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/573f9b99acadc86b5c7f9eb1c95e5d5f8f879b22

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Stabilization for the semilinear wave equation with geometric control condition (2012, methodology): “Writing and using the local elliptic regularity properties (see [42] and the references therein for example), we get that u ∗ is locally of class C 2 ,λ in space for some λ ∈ (0 , 1).”
A unified approach to universal inequalities for eigenvalues of elliptic operators (2004, background): “Ashbaugh and Benguria produced the earliest " parameterfree " proof of the HP inequality in [7].”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “Nonlinear elliptic equation, singularity, boundary blow-up, bifurcation, asymptotic anal- ysis, maximum principle, Karamata regular variation theory.”
Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold (2007, methodology): “ha l- 00 14 52 50 , v er si on 1 - 9 M ay 2 00 7 As an application, we obtain a characterization of critical domains of the trace of the heat kernel under Dirichlet boundary conditions.”
Asymptotic behavior of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach (2007, background): “Then we have the following result of classical potential theory (cf, Miranda 26 , 27 , see also 24 , Theorem 3.”
Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem (2005, background): “p.1 see e.g. [ 3 ] and references therein. However, discretization of the BDIE leads then to a dense system of linear algebraic equations, and hence prevents the use of economical methods that are available for sparse systems.”