On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation
Jan Bochenek (1965)
Annales Polonici Mathematici
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Displaying similar documents to “The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains”
On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation
Positive solutions for sublinear elliptic equations
Bogdan Przeradzki, Robert Stańczy (2002)
Colloquium Mathematicae
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The existence of a positive radial solution for a sublinear elliptic boundary value problem in an exterior domain is proved, by the use of a cone compression fixed point theorem. The existence of a nonradial, positive solution for the corresponding nonradial problem is obtained by the sub- and supersolution method, under an additional monotonicity assumption.
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.
On the differentiability of weak solutions of certain non-elliptic equations II
H. Marcinkowska (1963)
Studia Mathematica
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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.
Semilinear Elliptic Equations on Unbounded Domains.
G.R. Burton (1985)
Mathematische Zeitschrift
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Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain
Mikhail Borsuk (2007)
Applicationes Mathematicae
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We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.
Weak compactness of solutions for fourth order elliptic systems with critical growth
Paweł Goldstein, Paweł Strzelecki, Anna Zatorska-Goldstein (2013)
Studia Mathematica
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We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.
On interior and boundary regularity of weak solutions to a certain quasilinear elliptic system.
Norbert Jakobowsky (1992)
Mathematische Zeitschrift
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The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part II)
Adam Kubica (2005)
Applicationes Mathematicae
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We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
Semilinear elliptic problems in unbounded domains
Aleksandra Orpel (2006)
Applicationes Mathematicae
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We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.
On existence of the weak solution for non-linear partial differential equations of elliptic type
Jozef Kačur (1970)
Commentationes Mathematicae Universitatis Carolinae
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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.