Wyniki wyszukiwania dla: ELLIPTIC PDE

• Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces

  Publikacja

  • J. Maksymiuk
  • K. Wroński

  - Topological Methods in Nonlinear Analysis - Rok 2020

  We consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.

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• Module structure in Conley theory with some applications

  Publikacja

  • Z. Dzedzej

  - BANACH CENTER PUBLICATIONS - Rok 2014

  A multiplicative structure in the cohomological versjon of Conley index is described . In the case of equivariant flows we apply the normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is then applied to obtain a mountain pass type theorem. Another application is a result on multiple bifurcations for some elliptic PDE.

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