Using ideas from the theory of Orlicz spaces, we discuss the Hölder regularity of a bounded weak solution of a p–Laplacian type parabolic partial differential equation under generalized structure conditions. To show the Hölder continuity of such solutions, we use the idea of spreading positivity and geometric characters besides the standard De Giorgi's iteration method. For showing Hölder 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.
|Advisor:||Lieberman, Gary M.|
|Commitee:||Hogben, Leslie, Liu, Hailiang, Sacks, Paul, Smiley, Michael|
|School:||Iowa State University|
|School Location:||United States -- Iowa|
|Source:||DAI-B 74/02(E), Dissertation Abstracts International|
|Keywords:||Generalized laplacian equation, Holder regularity, Laplacian equations, Orlicz space, Parabolic equation, Partial differential equation|
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