Integrals of the Calculus of Variations with p, q-growth may have not smooth minimizers, not
even bounded, for general p, q exponents. In this paper we consider the scalar case, which …

This paper deals with existence and regularity in variational problems related to partial
differential equations and systems-both in the elliptic and in the parabolic contexts-and to …

We consider variational solutions to the Cauchy-Dirichlet problem∂ tu= div D ξ f (x, u, D u)−
D uf (x, u, D u) in Ω T u= u 0 on∂ par Ω T where the function f= fx, u, ξ, f: R n× RN× RN× …

We establish the higher differentiability of integer order of solutions to a class of obstacle
problems assuming that the gradient of the obstacle possesses an extra integer …

We study the Neumann and Dirichlet problems for the total variation flow in doubling metric
measure spaces supporting a weak Poincaré inequality. We prove existence and …

In this paper we would like to complement the results contained in Gavioli (Forum Math, to
appear) by dealing with the higher differentiability of integer order of solutions to a class of …

We here establish the higher fractional differentiability for solutions to a class of obstacle
problems with non-standard growth conditions. We deal with the case in which the solutions …

In this work we give optimal, ie, necessary and sufficient, conditions for integrals of the
calculus of variations to guarantee the existence of solutions---both weak and variational …

In this paper we present a variational approach to establish the existence and uniqueness of
variational solutions to nonlocal evolutionary problems. The model we have in mind is the …

Anisotropic partial differential equations recently received a large interest in the
mathematical literature, due to their applications to double and multiphase variational …