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.

A family of degenerate elliptic operators: maximum principle and its consequences / Birindelli, Isabella; Galise, Giulio; Hitoshi, Ishii. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 35:(2018), pp. 417-441. [10.1016/j.anihpc.2017.05.003]

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

BIRINDELLI, Isabella;GALISE, GIULIO;
2018

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.
2018
Equazioni ellittiche degeneri; principio del massimo; regolarità Lipschitz
01 Pubblicazione su rivista::01a Articolo in rivista
A family of degenerate elliptic operators: maximum principle and its consequences / Birindelli, Isabella; Galise, Giulio; Hitoshi, Ishii. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 35:(2018), pp. 417-441. [10.1016/j.anihpc.2017.05.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/966007
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