arXiv:2104.02407 Abstract | arXiv Analytics

arXiv:2104.02407 [math.AP]Abstract References Reviews Resources

Mixed boundary value problems for fully nonlinear degenerate or singular equations

Isabeau Birindelli, Francoise Demengel, Fabiana Leoni

Published 2021-04-06Version 1

We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global H\"older estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems.

Comments: 31 pages

Categories: math.AP

Subjects: 35J66, 35J70, 35J75

Keywords: mixed boundary value problems, fully nonlinear degenerate, singular equations, degenerate elliptic equations, ad hoc barriers

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