In this paper we study the regularity of the solutions of viscosity solutions of the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in } \Omega\subset \R\times \R^{n}\, .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\R^n)$ is uniformly convex, we prove that the gradient $D_{x}u$ belongs to the class $SBV_{loc}(\Omega)$.
SBV Regularity for Hamilton-Jacobi Equations in ℝn / Bianchini, S.; DE LELLIS, Camillo; Robyr, R.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 200:3(2011), pp. 1003-1021. [10.1007/s00205-010-0381-z]
SBV Regularity for Hamilton-Jacobi Equations in ℝn
Bianchini, S.;DE LELLIS, Camillo;
2011-01-01
Abstract
In this paper we study the regularity of the solutions of viscosity solutions of the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in } \Omega\subset \R\times \R^{n}\, .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\R^n)$ is uniformly convex, we prove that the gradient $D_{x}u$ belongs to the class $SBV_{loc}(\Omega)$.File in questo prodotto:
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