Sobolev regularity for quasilinear parabolic equations with asymptotically regular nonlinearity. (English) Zbl 1448.35315
Summary: We prove an interior Calderón-Zygmund type estimate in Sobolev space for the spatial gradient of weak solutions to quasilinear parabolic equations with an asymptotically regular nonlinearity by constructing a regular problem via Poisson’s formula. In addition, the nonlinearity is also assumed to satisfy the uniform ellipticity, \(p\)-growth and local Lipschitz continuity conditions in the unknown function.
MSC:
| 35K59 | Quasilinear parabolic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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