Nonlinear anisotropic parabolic equations in \(L^m\). (English) Zbl 1377.35166
Summary: In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an \(L^m\) function, with \(m\) being “small”. This work generalizes some results given in [L. Boccardo et al., J. Funct. Anal. 147, No. 1, 237–258 (1997; Zbl 0887.35082)] and [F. Q. Li, J. Convex Anal. 8, No. 2, 417–422 (2001; Zbl 1004.35052)].
MSC:
| 35K59 | Quasilinear parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
References:
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