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

Mathematics – Optimization and Control

Scientific paper

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Scientific paper

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 H\"older continuous with H\"older exponent depending only
on the growth of the Hamiltonian. The proof relies on a reverse H\"older
inequality.

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