Local existence for parabolic problems with fully nonlinear boundary condition; an \(L_ p\)-approach

DOI10.1007/BF01764128zbMath0762.35046MaRDI QIDQ1191388

Peter Weidemaier

Publication date: 27 September 1992

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

global uniqueness theorem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Initial-boundary value problems for second-order parabolic equations (35K20) Variational methods applied to PDEs (35A15)

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Cites Work

• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Parabolic equations with nonlinear time-dependent boundary conditions
• Quasilinear parabolic systems under nonlinear boundary conditions
• Local existence for quasilinear parabolic systems under nonlinear boundary conditions
• The linearization principle for the stability of solutions of quasilinear parabolic equations. I
• Refinement of an \(L^ p\)-estimate of Solonnikov for a parabolic equation of the second order with conormal boundary condition
• Nonhomogeneous initial-boundary value problems for linear parabolic systems
• On pababolic oblique derivative problem with holder continuous coefficients
• Global existence for semilinear parabolic systems.
• Maximal space regularity in nonhoomogeneous initial boundary value parabolic problem
• Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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