In this paper we study the regularity of the solutions of viscosity solutionsof 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
DE LELLIS, Camillo;
2011-01-01
Abstract
In this paper we study the regularity of the solutions of viscosity solutionsof 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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