We establish a series of optimal regularity results for solutions to general non-linear
parabolic systems\[u_t-\mathrm {div}\a (x, t, u, Du)+ H= 0\,,\] under the main assumption of …

We prove that, if u: Ω ⊂ R^ n → R^ N is a solution to the Dirichlet variational problem\rm min
w Ω F (x, w, Dw)\rm dx\rm subject\, to\quad w ≡ u_0\rm on\; ∂ Ω, involving a regular …

The aim of the paper is twofold. On one hand we want to present a new technique called $ p
$-caloric approximation, which is a proper generalization of the classical compactness …

We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of
variation form when the nonlinearity is allowed to be discontinuous and the boundary of the …

Harmonic type approximation lemmas Page 1 J. Math. Anal. Appl. 352 (2009) 301–335 www.elsevier.com/locate/jmaa
Harmonic type approximation lemmas Frank Duzaara, Giuseppe Mingioneb,∗ a Institute for …

We consider parabolic equations of the type ut− divA (x, t, Du)= μ having a Radon measure
on the right-hand side and prove fractional integrability and differentiability results of …

We consider the following prototype problem:{&-Δ u+ M| ∇ u|^ 2 u^ θ= f& in\varOmega\&u=
0& on\partial\varOmega.-Δ u+ M|∇ u| 2 u θ= f in Ω u= 0 on∂ Ω and we study the regularity of …

This is the second part of a work aimed at establishing that for solutions to Cauchy–Dirichlet
problems involving general non-linear systems of parabolic type, almost every parabolic …

This paper concerns a Fokker-Planck equation on the positive real line modeling nucleation
and growth of clusters. The main feature of the equation is the dependence of the driving …

We establish a partial regularity result for weak solutions of nonsingular parabolic systems
with subquadratic growth of the type∂ tu− div a (x, t, u, Du)= B (x, t, u, Du), where the …