On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation

Jan Bochenek

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Displaying similar documents to “On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation”

Generalized Maximum Principle for Divergence Form Elliptic Equations in Unbounded Domains

Maurizio Chicco (2009)

Bollettino dell'Unione Matematica Italiana

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In this note I extend some previuos results concerning a generalized maximum principle for linear second order elliptic equations in divergence form, to the case of unbounded domains.

An overdetermined elliptic problem in a domain with countably rectifiable boundary

Przemysław Górka (2007)

Colloquium Mathematicae

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We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.

Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point

Mikhail Borsuk, Krzysztof Żyjewski (2011)

Applicationes Mathematicae

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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.

Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields

Xiangxing Tao (2002)

Studia Mathematica

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Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.

Semilinear Elliptic Equations on Unbounded Domains.

G.R. Burton (1985)

Mathematische Zeitschrift

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A fictitious domain approach to the numerical solution of elliptic boundary value problems defined in stochastic domains

Canuto, Claudio, Kozubek, Tomáš

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On some elliptic boundary-value problems with discontinuous nonlinearities

Giovanni Anello (2005)

Annales Polonici Mathematici

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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.

On quasilinear elliptic equations in domains with conical boundary points.

Manfred Dobrowolski (1989)

Journal für die reine und angewandte Mathematik

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On the Green's function for second order elliptic differential equations

B. Szafirski (1967)

Colloquium Mathematicae

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The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Damian Wiśniewski (2016)

Annales Mathematicae Silesianae

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We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Elliptic and degenerate-elliptic operators in unbounded domains

D. E. Edmunds, W. D. Evans (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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An abstract version of the resonance theorem

B. Przeradzki (1991)

Annales Polonici Mathematici

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Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Mikhail Borsuk (1998)

Annales Polonici Mathematici

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We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.