Definition 1 implies that local minimisers are automatically in W 1, p loc (Ω). We immediately
say that since all the regularity properties of local minimisers treated in this paper are local in …

Regularity of minima: An invitation to the dark side of the calculus of variations | SpringerLink
Skip to main content Advertisement SpringerLink Log in Menu Find a journal Publish with us …

Gradient estimates via non-linear potentials Page 1 Gradient estimates via non-linear
potentials Frank Duzaar, Giuseppe Mingione American Journal of Mathematics, Volume 133 …

We show how to infer sharp partial regularity results for relaxed minimizers of degenerate,
nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theory. In …

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 …

Abstract Let Ω⊂R^n, n\geq2, be a bounded domain withboundary ∂Ω, and Q=Ω*(0,T be a
cylinder of height Ts<∞. We study local weak solutions of the parabolic equation Lu≡∂u∂t …

We extend to the degenerate case p\not=2, Simon's approach to the classical regularity
theory of harmonic maps of Schoen & Uhlenbeck, by proving a “p-Harmonic Approximation …

We study the Dirichlet problem for the elliptic equations in a bounded domain Ω⊂ Rn, and
the class of elliptic systems u=(u (1),…, u (n)), satisfying the growth condition [Formula: see …

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 …

Publisher Summary This chapter discusses the theory of elliptic equations with nonstandard
growth conditions and systems of such equations. It discusses the questions of existence …