A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

2008/02/21 by Pierre Cardaliaguet, Cardaliaguet, Pierre
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.0802.3153

arxiv created 2008/02/21 · arxiv updated 2009/12/01

Abstract

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.

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