Regularity and variationality of solutions  to Hamilton-Jacobi equations. 
Part I: Regularity 
(errata)

Andrea C. G. Mennucci

Displaying similar documents to “Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity (errata)”

Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I : regularity

Andrea C. G. Mennucci (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We formulate an Hamilton-Jacobi partial differential equation $H (x, D u (x)) = 0$ on a $n$ dimensional manifold $M$ , with assumptions of convexity of $H (x, \cdot)$ and regularity of $H$ (locally in a neighborhood of ${H = 0}$ in $T^{*} M$ ); we define the “min solution” $u$ , a generalized solution; to this end, we view $T^{*} M$ as a symplectic manifold. The definition of “min solution” is suited to proving regularity results about $u$ ; in particular, we prove in the first part that the closure of the set where $u$ is not regular...

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

Pierre Cardaliaguet (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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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.