Geodesic
A family of degenerate elliptic operators: Maximum principle and its consequences
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 417-441

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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.

DOI : 10.1016/j.anihpc.2017.05.003
Classification : 35J60, 35J70, 49L25
Keywords: Maximum principle, Fully nonlinear degenerate elliptic PDE, Eigenvalue problem 
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     title = {A family of degenerate elliptic operators: {Maximum} principle and its consequences},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {417--441},
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Birindelli, Isabeau; Galise, Giulio; Ishii, Hitoshi. A family of degenerate elliptic operators: Maximum principle and its consequences. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 417-441. doi: 10.1016/j.anihpc.2017.05.003

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