☆ 4.4 Article

Lipschitz bounds for integral functionals with (p, q)-growth conditions

ADVANCES IN CALCULUS OF VARIATIONS (2022)

Related references

Note: Only part of the references are listed.

Article Mathematics, Applied

Maximal regularity for local minimizers of non-autonomous functionals

Peter Hasto et al.

Summary: This study establishes a sharp and general regularity theory for functionals, solving an open problem since the 1980s. Unlike previous results, a concise way of expressing the continuity requirement is used, applicable to various growth conditions.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2022)

Add to Collection

Article Mathematics, Applied

Borderline Lipschitz regularity for bounded minimizers of functionals with (p, q)-growth

Karthik Adimurthi et al.

Summary: We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard ( p, q)-growth in the Lorentz space L(N, 1), extending recent work by Beck and Mingione with weaker assumptions. Our result is sharp for certain special ranges of p, q, and N.

FORUM MATHEMATICUM (2022)

Add to Collection

Article Mathematics, Applied

Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations

Peter Bella et al.

Summary: In this study, we investigate the local regularity properties of solutions of linear, nonuniformly elliptic equations by assuming certain integrability conditions on the coefficient field. We prove local boundedness and Harnack inequality, and apply the deterministic regularity results to the corrector equation in stochastic homogenization, establishing sublinearity of the corrector.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2021)

Add to Collection

Article Mathematics, Applied

Growth conditions and regularity, an optimal local boundedness result

Jonas Hirsch et al.

Summary: The local boundedness of local minimizers of scalar integral functionals is proven for integrals over subsets of Rn where the integrand satisfies (p, q)-growth conditions. The optimal relation is maintained during the proof, showing the importance of these growth conditions.

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS (2021)

Add to Collection

Article Mathematics, Applied

Growth conditions and regularity for weak solutions to nonlinear elliptic pdes

Paolo Marcellini

Summary: The article focuses on the interior regularity of weak solutions to a class of nonlinear elliptic equations and minimizers of integrals of the calculus of variations. It highlights differences between solving equations and minimizing energy integrals, as well as between x-dependence and x-independence.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

Add to Collection

Article Mathematics

Boundary regularity for manifold constrained p(x)-harmonic maps

Iwona Chlebicka et al.

Summary: The article demonstrates the partial and full boundary regularity for p(x)-harmonic maps constrained by manifolds.

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2021)

Add to Collection

Article Mathematics, Applied

Global higher integrability for minimisers of convex functionals with (p,q)-growth

Lukas Koch

Summary: In this study, we proved the global W1,q(Omega,Rm) regularity for minimizers of convex functionals F(u)=integral Omega F(x,Du)dx, and also demonstrated the same regularity for minimizers of the associated relaxed functional. Our main assumptions on F(x, z) include a uniform alpha-Holder continuity assumption in x and controlled (p, q)-growth conditions in z with q(n+alpha)pn.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2021)

Add to Collection

Article Mathematics, Applied

Higher integrability for variational integrals with non-standard growth

Mathias Schaeffner

Summary: This study examines the properties of autonomous integral functionals of a specific form, establishing higher gradient integrability and partial regularity for minimizers under certain conditions, thus improving upon earlier results.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2021)

Add to Collection

Article Mathematics, Applied

Lipschitz Bounds and Nonautonomous Integrals

Cristiana De Filippis et al.

Summary: The study presents a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity, ranging from unbalanced polynomial growth conditions to fast, exponential growth. The sharp results obtained are optimal with respect to all considered data, and also provide new regularity criteria in the classical uniformly elliptic case. Furthermore, a classification of different types of nonuniform ellipticity is given, along with suitable conditions to obtain regularity theorems.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

Add to Collection

Article Mathematics, Applied

Recent developments in problems with nonstandard growth and nonuniform ellipticity

Giuseppe Mingione et al.

Summary: This paper provides an overview of recent results on elliptic variational problems with nonstandard growth conditions and related to different kinds of nonuniformly elliptic operators, with a focus on regularity theory.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

Add to Collection

Article Mathematics, Applied

Lipschitz regularity for degenerate elliptic integrals with p, q-growth

Giovanni Cupini et al.

Summary: In this study, we established the local Lipschitz continuity and higher differentiability of vector-valued local minimizers of a class of energy integrals in the Calculus of Variations. An important aspect of our work is dealing with potentially degenerate energy densities with respect to the x-variable.

ADVANCES IN CALCULUS OF VARIATIONS (2021)

Add to Collection

Article Mathematics, Applied

Regularity for scalar integrals without structure conditions

Michela Eleuteri et al.

ADVANCES IN CALCULUS OF VARIATIONS (2020)

Add to Collection

Article Mathematics

On the Regularity of Minima of Non-autonomous Functionals

Cristiana De Filippis et al.

JOURNAL OF GEOMETRIC ANALYSIS (2020)

Add to Collection

Article Mathematics, Applied

Lipschitz Bounds and Nonuniform Ellipticity

Lisa Beck et al.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2020)

Add to Collection

Article Mathematics, Applied

New Examples on Lavrentiev Gap Using Fractals

Anna Kh. Balci et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2020)

Add to Collection

Article Mathematics, Applied

REGULARITY RESULTS FOR GENERALIZED DOUBLE PHASE FUNCTIONALS

Sun-Sig Byun et al.

ANALYSIS & PDE (2020)

Add to Collection

Article Mathematics, Applied

ON THE REGULARITY OF MINIMIZERS FOR SCALAR INTEGRAL FUNCTIONALS WITH (p, q)-GROWTH

Peter Bella et al.

ANALYSIS & PDE (2020)

Add to Collection

Article Mathematics

Lipschitz regularity results for a class of obstacle problems with nearly linear growth

Giacomo Bertazzoni et al.

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS (2020)

Add to Collection

Article Mathematics, Applied

A proof of the Krylov-Safonov theorem without localization

Connor Mooney

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2019)

Add to Collection

Article Mathematics, Applied

Regularity for general functionals with double phase

Paolo Baroni et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2018)

Add to Collection

Article Mathematics, Applied

Holder regularity of quasiminimizers under generalized growth conditions

Petteri Harjulehto et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2017)

Add to Collection

Article Mathematics

Global Lipschitz continuity for minima of degenerate problems

Pierre Bousquet et al.

MATHEMATISCHE ANNALEN (2016)

Add to Collection

Article Mathematics, Applied

Regularity for Double Phase Variational Problems

Maria Colombo et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2015)

Add to Collection

Article Mathematics, Applied

Riesz potential estimates for a general class of quasilinear equations

Paolo Baroni

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2015)

Add to Collection

Article Mathematics, Applied

A nonlinear Stein theorem

Tuomo Kuusi et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2014)

Add to Collection

Article Mathematics, Applied

Linear Potentials in Nonlinear Potential Theory

Tuomo Kuusi et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2013)

Add to Collection

Article Mathematics, Applied

Higher differentiability of minimizers of convex variational integrals

Menita Carozza et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2011)

Add to Collection

Article Mathematics, Applied

Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations

Andrea Cianchi et al.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2011)

Add to Collection

Article Mathematics

Sharp regularity for functionals with (p, q) growth

L Esposito et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2004)

Add to Collection

Article Multidisciplinary Sciences

Non-Lipschitz minimizers of smooth uniformly convex functionals

V Sverák et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2002)

Add to Collection

© Peeref 2019-2024. All rights reserved.