Lipschitz regularity for viscous Hamilton-Jacobi equations with Lp terms期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Lipschitz regularity for viscous Hamilton-Jacobi equations with Lp terms

Affiliation:	1. Dipartimento di Scienze Matematiche Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy;2. Gran Sasso Science Institute, viale Francesco Crispi 7, 67100 L''Aquila, Italy;1. Robert H. Smith School of Business, University of Maryland, United States;2. Department of Mathematics, Imperial College London, United Kingdom;3. Faculty of Mathematics and Economics, University of Ulm, Germany;1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;2. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, PR China;1. Università degli Studi di Napoli “Federico II”, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Via Cintia, 80126 Napoli, Italy;2. Sapienza Università di Roma, Dipartimento di Matematica “G. Castelnuovo”, P.le A. Moro 1, 00185 Roma, Italy

Abstract:	We provide Lipschitz regularity for solutions to viscous time-dependent Hamilton-Jacobi equations with right-hand side belonging to Lebesgue spaces. Our approach is based on a duality method, and relies on the analysis of the regularity of the gradient of solutions to a dual (Fokker-Planck) equation. Here, the regularizing effect is due to the non-degenerate diffusion and coercivity of the Hamiltonian in the gradient variable.

Keywords:	Hamilton-Jacobi equations with unbounded data Lipschitz regularity Kardar-Parisi-Zhang Adjoint method
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