Some uniqueness results for Bernoulli interior free-boundary problems in convex domains.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
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.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
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.
On the approximation of front propagation problems with nonlocal terms
We investigate the approximation of the evolution of compact hypersurfaces of depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.
Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations
Representation of equilibrium solutions to the table problem of growing sandpiles
In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...
On the approximation of front propagation problems with nonlocal terms
We investigate the approximation of the evolution of compact hypersurfaces of depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.
Equilibria and strict equilibria of multivalued maps on noninvariant sets
This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed.
Information issues in differential game theory
In this survey paper we present recent advances in some classes of differential game in which there is an asymmetry of information between the players. We explain that—under suitable structure conditions—these games have a value, which can be characterized in terms of (new) Hamilton-Jacobi equations.
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