We prove local supremum bounds, a Harnack inequality, Hölder continuity up to the boundary, and a strong maximum principle for solutions to a variational equation defined by an elliptic operator which becomes degenerate along a portion of the domain boundary and where no boundary condition is prescribed, regardless of the sign of the Fichera function. In addition, we prove Hölder continuity up to the boundary for solutions to variational inequalities defined by this boundary-degenerate elliptic operator.
|Original language||English (US)|
|Number of pages||55|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - May 29 2017|
Bibliographical noteFunding Information:
PF was partially supported by NSF grant DMS-1059206.
© 2016 Elsevier Masson SAS
- Degenerate diffusion process
- Degenerate elliptic differential operator
- Harnack inequality
- Hölder continuity
- Variational inequality
- Weighted Sobolev space