1,721,078 research outputs found
Regularity for multi-phase variational problems
Full text linkDe Filippis C, Oh J. Regularity for multi-phase variational problems. JOURNAL OF DIFFERENTIAL EQUATIONS. 2019;267(3):1631-1670.We prove C-1,C-nu -regularity for local minimizers of the multi-phase energy: w bar right arrow integral(Omega)vertical bar Dw vertical bar(p)+a(x)vertical bar Dw vertical bar(q)+b(x)vertical bar Dw vertical bar(s)dx, under sharp assumptions relating the couples (p, q) and (p, s) to the Holder exponents of the modulating coefficients a(.) and b(.), respectively. (C) 2019 Elsevier Inc. All rights reserved
Gradient bounds for solutions to irregular parabolic equations with (p, q)-growth
No full textWe provide quantitative gradient bounds for solutions to certain parabolic equations with unbalanced polynomial growth and non-smooth coefficients
Regularity results for a class of non-autonomous obstacle problems with (p,q)-growth
No full textWe study some regularity issues for solutions of non-autonomous obstacle problems with (p,q)-growth. Under suitable assumptions, our analysis covers the main models available in the literature
Partial regularity for manifold constrained p(x)-harmonic maps
Full text linkWe prove that manifold constrained p(x)-harmonic maps are locally C1,β0-regular outside a set of zero n-dimensional Lebesgue’s measure, for some β∈ (0 , 1). We also provide an estimate from above of the Hausdorff dimension of the singular set
On the regularity of the ω-minima of φ-functionals
Full text linkWe focus on some regularity properties of -minima of variational integrals with -growth and provide an upper bound on the Hausdorff dimension of their singular set
Regularity for solutions of fully nonlinear elliptic equations with nonhomogeneous degeneracy
Full text linkWe prove that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally C1, γ-regular
Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension
Full text linkWe prove higher summability for the gradient of minimizers of strongly convex
integral functionals of the Calculus of Variations
ˆ
Ω
f(x, Du(x)) dx, u : Ω ⊂ R
n → S
N−1
,
with growth conditions of (p, q)-type:
|ξ|
p ≤ f(x, ξ) ≤ C(|ξ|
q + 1), p < q,
in low dimension. Our procedure is set in the framework of Fractional Sobolev
Spaces and renders the desired regularity as the result of an approximation technique
relying on estimates obtained through a careful use of difference quotients
Optimal gradient estimates for multi-phase integrals
Full text linkWe prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems
Fully nonlinear free transmission problems with nonhomogeneous degeneracies
No full textWe prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies
Quasiconvexity and partial regularity via nonlinear potentials
No full textWe show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theory. In particular, in the setting of functionals with (p, q)growth - according to the terminology of Marcellini [52] - we derive optimal local regularity criteria under minimal assumptions on the data. (c) 2022 Elsevier Masson SAS. All rights reserved
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