کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4589819 | 1334912 | 2015 | 46 صفحه PDF | دانلود رایگان |
We consider the solvability of quasi-linear elliptic equations with either local or nonlocal Neumann, Robin, or Wentzell boundary conditions, defined (in the generalized sense) on a bounded W1,pW1,p-extension domain whose boundary is an upper d -set, for an appropriate d≥0d≥0. Then, we extend the fine regularity theory for weak solutions of the elliptic equations with the above boundary conditions, known for bounded Lipschitz domains, to bounded W1,pW1,p-extension domains whose boundaries are upper d-sets, by showing that such weak solutions are globally Hölder continuous. Consequently, we generalize substantially the class of bounded domains where weak solutions of boundary value problems of type Neumann, Robin, or Wentzell, may be uniformly continuous (up to the boundary).
Journal: Journal of Functional Analysis - Volume 269, Issue 1, 1 July 2015, Pages 1–46