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Using ideas from the theory of Orlicz spaces, we discuss the Holder regularity of a bounded weak solution of a p−Laplacian type parabolic partial differential equation under generalized structure conditions. To show the Holder continuity of such solutions, we use the idea of spreading positivity and geometric characters besides the standard De Giorgi’s iteration method. For showing Holder continuity of Du, we follow the perturbation argument. Under the generalized structure conditions, we give a uniform method of proof in an intrinsically scaled cylinder without separating degenerate and singular cases.

Holder regularity of solutions of generalized p-Laplacian type parabolic equations