Under usual assumptions on the Hamiltonian, we prove that any viscosity solution of the corresponding Hamilton-Jacobi equation on the manifold M is locally semiconcave and C loc outside the closure of its singular set (which is nowhere dense in M). Moreover, we prove that, under additional assumptions and in low dimension, any viscosity solution of that Hamilton-Jacobi equation satisfies a gene...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

Abstract We consider a quasilinear degenerate parabolic equation driven by the orthotropic p -Laplacian. prove that local weak solutions are locally Lipschitz continuous in spatial variable, uniformly time.

In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The is realized by combining a theoretical result regarding the computation of directions nonsmooth MOPs with practical to approximate subdifferentials objective functions. We show convergence points which satisfy necessary condition Pareto optimality. Using set ...