1,721,039 research outputs found
Optimal Lipschitz criteria and local estimates for nonuniformly elliptic problems
No full textWe report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for Lipschitz continuity known in the uniformly elliptic one and provide a unified approach between non-uniformly and uniformly elliptic problems
Recent developments in problems with nonstandard growth and nonuniform ellipticity
No full textWe provide an overview of recent results concerning elliptic variational problems with nonstandard growth conditions and related to different kinds of nonuniformly elliptic operators. Regularity theory is at the center of this paper
Full C1, α-regularity for minimizers of integral functionals with L log L-growth
No full textWe consider the integral functional with nearly-linear growth int;Ω |Du| log(1+|Du|)dx where u : Ω ⊂ Rn → RN (n ≥ 2, N ≥ 1) and we prove that any local minimizer u has locally Hölder continuous gradient in the interior of Ω thus excluding the presence of singular sets in Ω. This functional has recently been considered by several authors in connection with variational models for problems from the theory of plasticity with logarithmic hardening. We also give extensions of this result to more general cases. © Heldermann Verlag
THE SHARP GROWTH RATE IN NONUNIFORMLY ELLIPTIC SCHAUDER THEORY
No full textSchauder estimates hold in nonuniformly elliptic problems under optimal assump-
tions on the growth of the ellipticity ratio
Lipschitz Bounds and Nonautonomous Integrals
Full text linkWe provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems
Interpolative gap bounds for nonautonomous integrals
No full textFor nonautonomous, nonuniformly elliptic integrals with so-called (p, q)-growth conditions, we show a general interpolation property allowing to get basic higher integrability results for Hölder continuous minimizers under improved bounds for the gap q/p. For this we introduce a new method, based on approximating the original, local functional, with mixed local/nonlocal functionals, and allowing for suitable estimates in fractional Sobolev spaces
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