Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Abstract: We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions, to our knowledge. If some eigenvalue is missing, such operators are nonlinear, degenerate, non-uniformly elliptic, neither convex nor concave. Here we prove an interior Lipschitz estimate under a non-standard assumption: that the solution exists in a larger, unbounded domain, and vanishes at infinity. In other words, we need a condition coming from far away. We also provide existence results showing that this condition is satisfied for a large class of solutions. On the occasion, we also extend a few qualitative properties of solutions, known for uniformly elliptic operators, to partial trace operators.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues ; volume:11 ; number:1 ; year:2022 ; pages:1182-1200 ; extent:19 ; Advances in nonlinear analysis ; 11, Heft 1 (2022), 1182-1200 (gesamt 19)

Contributors, Places and Time

• Creator: Vitolo, Antonio

Further information

• DOI: 10.1515/anona-2022-0241
• URN: urn:nbn:de:101:1-2022072014163484612224
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:36 AM CEST