Boundedness and continuity of solutions to linear elliptic boundary value problems in two dimensions

DOI10.1007/BF01459758zbMath0790.35025OpenAlexW365669208MaRDI QIDQ1322078

Konrad Gröger

Publication date: 9 June 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165193

zbMATH Keywords

Sobolev spacescontinuityboundednessmixed boundary value problemsbounded two-dimensional Lipschitzian domainlinear second order elliptic differential equationsnew interpolation spaces

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Interpolation between normed linear spaces (46B70)

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Cites Work

• Semigroups of linear operators and applications to partial differential equations
• A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
• Resolvent estimates in \(W^{-1,p}\) for second order elliptic differential operators in case of mixed boundary conditions
• Continuity of solutions of uniformly elliptic equations in \(\mathbb{R}^ 2\)
• Improved regularity of solutions to elliptic equations involving Jacobians and applications
• Higher integrability of determinants and weak convergence in L1.
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