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September/October 2022 Double phase obstacle problems with variable exponent
Shengda Zeng, Vicențiu D. Rădulescu, Patrick Winkert
Adv. Differential Equations 27(9/10): 611-645 (September/October 2022).

Abstract

This paper is devoted to the study of a quasilinear elliptic inclusion problem driven by a double phase differential operator with variable exponents, an obstacle effect and a multivalued reaction term with gradient dependence. By using an existence result for mixed variational inequalities with multivalued pseudomonotone operators and the theory of nonsmooth analysis, we examine the nonemptiness, boundedness and closedness of the solution set to the problem under consideration. In the second part of the paper, we present some convergence analysis for approximated problems. To be more precise, when the obstacle function is approximated by a suitable sequence, applying a generalized penalty technique, we introduce a family of perturbed problems without constraints associated to our problem and prove that the solution set of the original problem can be approached by the solution sets of the perturbed problems in the sense of Kuratowski.

Citation

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Shengda Zeng. Vicențiu D. Rădulescu. Patrick Winkert. "Double phase obstacle problems with variable exponent." Adv. Differential Equations 27 (9/10) 611 - 645, September/October 2022.

Information

Published: September/October 2022
First available in Project Euclid: 2 June 2022

Subjects:
Primary: 35J20 , 35J25 , 35J60 , 35R70

Rights: Copyright © 2022 Khayyam Publishing, Inc.

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Vol.27 • No. 9/10 • September/October 2022
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