On the Boundedness of Solutions of Degenerate Anisotropic Elliptic Variational Inequalities

Gorban, Yuliya; Kovalevsky, Alexander A.

doi:10.1007/s00025-013-0334-6

Cited by 6 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the last decades, increasing attention has been given to the investigation of existence and properties of solutions to various problems for integral functionals with anisotropic integrands and for elliptic equations and variational inequalities with anisotropic coefficients (see for instance [1][2][3][4][5][6][7][8][9][10][11]13,15]). On the whole, the study of these problems requires more delicate procedures as compared with those used in the isotropic case.…”

Section: Introduction and Exposition Of Known Resultsmentioning

confidence: 99%

Integrability and boundedness of solutions to some anisotropic problems

Kovalevsky

2015

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

In this article, we give a series of results on the improved integrability and boundedness of solutions to several anisotropic problems. In particular, we consider the nonhomogeneous Dirichlet problem for anisotropic elliptic second-order equations. Moreover, we study anisotropic variational inequalities with unilateral and bilateral obstacles as well as gradient constraints. Finally, variational problems for integral functionals with anisotropic integrands are considered.

show abstract

Section: Introduction and Exposition Of Known Resultsmentioning

confidence: 99%

Integrability and boundedness of solutions to some anisotropic problems

Kovalevsky

2015

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Concerning degenerated elliptic operators of high order we refer to a work of the same authors [21]. Recently, Gorban-Kovalevsky [16] have been studied the boundedness of solutions of degenerate anisotropic elliptic variational inequalities under certain conditions on the right-hand side and the set of constraints. c) In case that K is the whole space V and j k (k = 1, 2) not necessarily smooth, problem (1.1) is a hemivariational inequality which contains as a special case the subsequent elliptic inclusion…”

Section: Introductionmentioning

confidence: 99%

On the Boundedness of Solutions to Elliptic Variational Inequalities

Winkert

2014

Set-Valued Var. Anal

View full text Add to dashboard Cite

Abstract. In this paper we present global a priori bounds for a class of variational inequalities involving general elliptic operators of second-order and terms of generalized directional derivatives. Based on Moser's and De Giorgi's iteration technique we prove the boundedness of solutions of such inequalities under certain criteria on the set of constraints. In our proofs we also use the localization method with a certain partition of unity and a version of a multiplicative inequality estimating the boundary integrals. Some sets of constraints satisfying the required conditions are stated as well.

show abstract

Improved integrability and boundedness of solutions to some high-order variational problems

Voitovych

2018

J Math Sci

View full text Add to dashboard Cite

On the Boundedness of Solutions of Degenerate Anisotropic Elliptic Variational Inequalities

Cited by 6 publications

References 6 publications

Integrability and boundedness of solutions to some anisotropic problems

Integrability and boundedness of solutions to some anisotropic problems

On the Boundedness of Solutions to Elliptic Variational Inequalities

Improved integrability and boundedness of solutions to some high-order variational problems

Contact Info

Product

Resources

About