L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems

Details L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems

2012-03-22

arxiv.org/abs/1203.4861v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

We prove boundedness of gradients of solutions to quasilinear parabolic system, the main part of which is a generalization to p-Laplacian and its right hand side's growth depending on gradient is not slower (and generally strictly faster) than p - 1. This result may be seen as a generalization to the classical notion of a controllable growth of right hand side, introduced by Campanato, over gradients of p-Laplacian-like systems. Energy estimates and nonlinear iteration procedure of a Moser type are cornerstones of the used method.

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