Some regularity results for basic systems of nonlinear parabolic type. (Italian. English summary) Zbl 0794.35019

Amato, Roberto

Atti Accad. Peloritana Pericolanti, Cl. Sci. Fis. Mat. Nat. 68, 387-399 (1990).

Summary: We show some regularity results for the solutions to nonlinear parabolic systems of the type \[ -\sum^ n_{i=1}D_ ia^ i(Du)+{\partial u\over\partial t}=0 \] assuming that the vector mappings \(p\to a^ i(p)\) have derivatives \(\partial a^ i(p)/\partial p^ j_ k\) which are continuous, but not uniformly continuous.

MSC:

35D10	Regularity of generalized solutions of PDE (MSC2000)
35K55	Nonlinear parabolic equations
35K40	Second-order parabolic systems