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Hölder-estimates for non-autonomous parabolic problems with rough data. (English) Zbl 1353.35095

Summary: In this paper we establish Hölder estimates for solutions to nonautonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of O. A. Ladyzhenskaya et al. [Linear and quasi-linear equations of parabolic type. Providence, RI: American Mathematical Society (AMS) (1968; Zbl 0174.15403)], which also serves as the starting point for our investigations.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data

Citations:

Zbl 0174.15403
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Full Text: DOI

References:

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