Some PDEs problems in generalized Sobolev algebras

DOI10.1016/j.jmaa.2011.07.063zbMath1246.35062OpenAlexW2080334521MaRDI QIDQ663613

Séverine Bernard, Silvère Paul Nuiro

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.07.063

zbMATH Keywords

generalized solutionsDirichlet problemColombeau algebrageneralized functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Weak solutions to PDEs (35D30) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Quasilinear elliptic equations (35J62)

Cites Work

• Nonlinear elliptic and parabolic equations involving measure data
• Multiplication of distributions. A tool in mathematics, numerical engineering and theoretical physics
• Topology on asymptotic algebras of generalized functions and applications
• Algebraic investigation of a nonlinear and singular Dirichlet problem
• On generalized Sobolev algebras and their applications
• Spectral asymptotic analysis in algebras of generalized functions
• Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions
• A nonlinear goursat problem with irregular data
• A contribution to the theory of generalized functions
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