Quasilinear Elliptic Equations with Small Boundary Data.
Chi-ping Lau (1985)
Manuscripta mathematica
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Displaying similar documents to “The exterior Dirichlet problem for quasi linear elliptic equations with small boundary data.”
Quasilinear Elliptic Equations with Small Boundary Data.
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We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate value property for such functions.
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Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms
Tomasz Klimsiak, Andrzej Rozkosz (2016)
Colloquium Mathematicae
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We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with...
On existence of a unique generalized solution to systems of elliptic PDEs at resonance
Tiantian Qiao, Weiguo Li, Kai Liu, Boying Wu (2014)
Annales Polonici Mathematici
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The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.
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On a Superlinear Elliptic Boundary Value Problem.
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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.