We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from Lp-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques à la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples.
Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method / Fabio Camilli, Alessandro Goffi, Cristian Mendico. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 2036-2145. - ELETTRONICO. - (In corso di stampa), pp. 0-0.
Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
Alessandro Goffi
;
In corso di stampa
Abstract
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from Lp-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques à la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples.
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Quantitative_rev_AnnaliSNS_v3Arxiv.pdf
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