The main result establishes that a weak solution of degenerate semilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate semilinear elliptic equations.

The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.

In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.

This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...

This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...

Integral representation of relaxed energies and of Γ-limits of functionals $$(u,v)\mapsto {\int }_{\Omega }f(x,u\left(x\right),v\left(x\right))dx$$ are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.

In questa nota dimostriamo stime asintotiche ottimali per le soluzioni deboli non negative del problema al contorno $$-{\mathrm{\Delta }}_{{\mathbb{H}}^n}u=u^{\left(Q+2\right)/\left(Q-2\right)}in\mathrm{\Omega },u=0\text{ in }\partial \mathrm{\Omega }.$$$-{\mathrm{\Delta }}_{{\mathbb{H}}^n}$

This paper is concerned with the Dirichlet-Cauchy problem for second order parabolic equations in domains with edges. The asymptotic behaviour of the solution near the edge is studied.