The local boundedness of gradients of weak solutions to elliptic and parabolic phi-Laplacian systems

In this thesis, a unified approach to prove the boundedness of gradients of solutions to degenerate and singular elliptic and parabolic phi-Laplacian systems is presented. At first, a Cacciopoli-type energy inequality with an additional function f which can be chosen freely is proven. Then, Di Giorg...

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Bibliographic Details
Published in:arXiv.org 2016-03
Main Author: Scharle, Toni
Format: Article
Language:English
Online Access:Get full text
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Summary:In this thesis, a unified approach to prove the boundedness of gradients of solutions to degenerate and singular elliptic and parabolic phi-Laplacian systems is presented. At first, a Cacciopoli-type energy inequality with an additional function f which can be chosen freely is proven. Then, Di Giorgi's method is applied using level sets which will lead to L-infinity-estimates on the gradient of the weak solution.
ISSN:2331-8422