Obstacle problem for a class of parabolic equations of generalized p-Laplacian type

Abstract

ABSTRACT. We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and that a uniformly bounded sequence of weak supersolutions converges to a weak supersolution. Moreover, we prove that if the obstacle is continuous, so is the solution.

The Cauchy–Dirichlet problem for a general class of parabolic equations

“…Novelties and technical tools. We believe that the main interest of this paper, apart from the results of Theorems 1.1 and 1.2 themselves (that will be used for instance in [31]), is the development of some tools for the treatment of the difficult equation (1.8) (see Paragraph 2.3). We prove the Lipschitz estimate as an a priori estimate for problems enjoying further regularity.…”