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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Jan Bochenek (1965)
Annales Polonici Mathematici
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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.
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.
H. Marcinkowska (1963)
Studia Mathematica
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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.
G.R. Burton (1985)
Mathematische Zeitschrift
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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.
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.
Norbert Jakobowsky (1992)
Mathematische Zeitschrift
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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.
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.
Jozef Kačur (1970)
Commentationes Mathematicae Universitatis Carolinae
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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.