Second-order regularity for parabolic \(p\)-Laplace problems. (English) Zbl 1439.35204
Summary: Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of \(p\)-Laplacian type, with square-integrable right-hand sides and initial data in a Sobolev space. As a consequence, generalized solutions are shown to be strong solutions. Minimal regularity on the boundary of the domain is required, though the results are new even for smooth domains. In particular, they hold in arbitrary bounded convex domains.
MSC:
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K65 | Degenerate parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
nonlinear parabolic equations; nonlinear parabolic systems; second-order derivatives; \(p\)-Laplacian; Cauchy-Dirichlet problems; convex domainsReferences:
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