JournalsaihpcVol. 35, No. 2pp. 417–441

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

  • Isabeau Birindelli

    Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, P.le Aldo Moro 2, I-00185 Roma, Italy

  • Giulio Galise

    Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, P.le Aldo Moro 2, I-00185 Roma, Italy

  • Hitoshi Ishii

    Faculty of Education and Integrated Arts and Sciences, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo 169-8050 Japan
A family of degenerate elliptic operators: Maximum principle and its consequences cover
Download PDF

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.

Cite this article

Isabeau Birindelli, Giulio Galise, Hitoshi Ishii, A family of degenerate elliptic operators: Maximum principle and its consequences. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 2, pp. 417–441

DOI 10.1016/J.ANIHPC.2017.05.003