A family of degenerate elliptic operators: Maximum principle and its consequences

By Isabeau Birindelli, G. Galise, Hitoshi Ishii. 2016

56 citations recorded by the source corpus.

Abstract In this paper we investigate the validity and the consequences of the maximum principle for degenerate elliptic operators whose higher order term is the sum of k eigenvalues of the Hessian. In particular we shed some light on some very unusual phenomena due to the degeneracy of the operator. We prove moreover Lipschitz regularity results and boundary estimates under convexity assumptions on the domain. As a consequence we obtain the existence of solutions of the Dirichlet problem and of principal eigenfunctions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2d851d919b85bf19b66a15f24983473a40a316f3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Julio D. Rossi
2. Pablo Blanc
3. Jorge García-Melián
4. Mayte Pérez-Llanos
5. Wenxian Shen

In Computational Theory and Mathematics

1. Julio D. Rossi
2. Pablo Blanc
3. Jorge García-Melián
4. Wenxian Shen
5. Mayte Pérez-Llanos

In Mathematical Physics

1. Julio D. Rossi
2. Pablo Blanc

Citations in the corpus

• Games for eigenvalues of the Hessian and concave/convex envelopes (2018, methodology): “In particular, we can handle equations of the form or a convex combination of the previous two These operators appear in [2, 3, 6, 7] and in [13, 14] with connections with geometry.”