PARTIAL REGULARITY OF THE MINIMIZERS OF QUADRATIC FUNCTIONALS WITH VMO COEFFICIENTS

MARIA ALESSANDRA RAGUSA; ATSUSHI TACHIKAWA

doi:10.1112/S002461070500699X

Abstract

The paper investigates the partial regularity of the minimizers for quadratic functionals whose integrands have VMO coefficients in principal part and nonlinear terms that are Carathéodory functions. We use some majorizations for the functional, rather than the well known Euler equation associated to it.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

RAGUSA, Maria Alessandra and TACHIKAWA, Atsushi 2005. On continuity of minimizers for certain quadratic growth functionals. Journal of the Mathematical Society of Japan, Vol. 57, Issue. 3,

Krylov, N.V. 2007. Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Journal of Functional Analysis, Vol. 250, Issue. 2, p. 521.

Byun, Sun-Sig and Wang, Lihe 2008. Gradient estimates for elliptic systems in non-smooth domains. Mathematische Annalen, Vol. 341, Issue. 3, p. 629.

Ragusa, Maria Tachikawa, Atsushi and Takabayashi, Hiroshi 2012. Partial regularity of 𝑝(𝑥)-harmonic maps. Transactions of the American Mathematical Society, Vol. 365, Issue. 6, p. 3329.

Ragusa, Maria Alessandra and Tachikawa, Atsushi 2013. On interior regularity of minimizers of -energy functionals. Nonlinear Analysis: Theory, Methods & Applications, Vol. 93, Issue. , p. 162.

Qiu, Dehua and Chen, Pingyan 2015. Complete moment convergence for product sums of sequence of extended negatively dependent random variables. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,

Foss, Mikil D. and Goodrich, Christopher S. 2016. On partial Hölder continuity and a Caccioppoli inequality for minimizers of asymptotically convex functionals between Riemannian manifolds. Annali di Matematica Pura ed Applicata (1923 -), Vol. 195, Issue. 5, p. 1405.

Ragusa, Maria Alessandra and Tachikawa, Atsushi 2016. On minimizers for functionals under the non-standard growth conditions. Vol. 1738, Issue. , p. 480112.

Goodrich, Christopher S. 2017. Partial Hölder continuity of minimizers of functionals satisfying a VMO condition. Advances in Calculus of Variations, Vol. 10, Issue. 1, p. 83.

Ragusa, Maria Alessandra and Tachikawa, Atsushi 2017. On the regularity in some variational problems. Vol. 1798, Issue. , p. 020128.

Goodrich, Christopher S. 2017. Partial Lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions. Journal of Differential Equations, Vol. 263, Issue. 7, p. 4400.

Goodrich, Christopher S. 2018. A general low-order partial regularity theory for asymptotically convex functionals with asymptotic dependence on the minimizer. Calculus of Variations and Partial Differential Equations, Vol. 57, Issue. 6,

Goodrich, Christopher S. 2018. Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems. Communications in Partial Differential Equations, Vol. 43, Issue. 11, p. 1599.

Goodrich, Christopher S. and Ragusa, M. Alessandra 2019. Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients. Nonlinear Analysis, Vol. 185, Issue. , p. 336.

Danecek, Josef and Viszus, Eugen 2020. Holder continuity for vector-valued minimizers of quadratic functionals. Electronic Journal of Differential Equations, Vol. 2020, Issue. 01-132, p. 69.

Goodrich, Christopher S. Alessandra Ragusa, M. and Scapellato, Andrea 2020. Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients. Journal of Differential Equations, Vol. 268, Issue. 9, p. 5440.

Nisar, Kottakkaran Sooppy Ali, Javaid Mahmood, Muhammad Khalid Ahmad, Daud and Ali, Shahbaz 2021. Hybrid evolutionary padé approximation approach for numerical treatment of nonlinear partial differential equations. Alexandria Engineering Journal, Vol. 60, Issue. 5, p. 4411.

Sarfraz, Naqash Filali, Doaa Hussain, Amjad Jarad, Fahd and Hong, Shaofang 2021. Weighted Estimates for Commutator of Roughp-Adic Fractional Hardy Operator on Weightedp-Adic Herz–Morrey Spaces. Journal of Mathematics, Vol. 2021, Issue. , p. 1.

Choucha, Abdelbaki Boulaaras, Salah Mahmoud Ouchenane, Djamel Allahem, Ali and Zaky, Mahmoud A. 2021. Global Existence for Two Singular One-Dimensional Nonlinear Viscoelastic Equations with respect to Distributed Delay Term. Journal of Function Spaces, Vol. 2021, Issue. , p. 1.

Saxena, Akanksha Argyros, Ioannis K. Jaiswal, Jai P. Argyros, Christopher and Pardasani, Kamal R. 2021. On the Local Convergence of Two-Step Newton Type Method in Banach Spaces under Generalized Lipschitz Conditions. Mathematics, Vol. 9, Issue. 6, p. 669.

Download full list

Article contents

PARTIAL REGULARITY OF THE MINIMIZERS OF QUADRATIC FUNCTIONALS WITH VMO COEFFICIENTS

Abstract

Keywords

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

PARTIAL REGULARITY OF THE MINIMIZERS OF QUADRATIC FUNCTIONALS WITH VMO COEFFICIENTS

Abstract

Keywords

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests