Publication detail

NONLOCAL DOUBLE PHASE IMPLICIT OBSTACLE PROBLEMS WITH MULTIVALUED BOUNDARY CONDITIONS

ZENG, S. RADULESCU, V. WINKERT, P.

Original Title

NONLOCAL DOUBLE PHASE IMPLICIT OBSTACLE PROBLEMS WITH MULTIVALUED BOUNDARY CONDITIONS

Type

journal article in Web of Science

Language

English

Original Abstract

In this paper, we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms, and an implicit obstacle constraint. Under very general assumptions on the data, we prove that the solution set of such an implicit obstacle problem is nonempty (so there is at least one solution) and weakly compact. The proof of our main result uses the Kakutani--Ky Fan fixed point theorem for multivalued operators along with the theory of nonsmooth analysis and variational methods for pseudomonotone operators.

Keywords

Clarke's generalized gradient; convection term; convex subdifferential; double phase problem; existence results; implicit obstacle; Kakutani-Ky Fan fixed point theorem; mixed boundary conditions; multivalued mapping

Authors

ZENG, S.; RADULESCU, V.; WINKERT, P.

Released

24. 3. 2024

ISBN

0036-1410

Periodical

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Year of study

56

Number

1

State

United States of America

Pages from

877

Pages to

912

Pages count

36

URL

https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001171826200020

BibTex

@article{BUT188261,
  author="Shengda {Zeng} and Vicentiu {Radulescu} and Patrick {Winkert}",
  title="NONLOCAL DOUBLE PHASE IMPLICIT OBSTACLE PROBLEMS WITH MULTIVALUED BOUNDARY CONDITIONS",
  journal="SIAM JOURNAL ON MATHEMATICAL ANALYSIS",
  year="2024",
  volume="56",
  number="1",
  pages="877--912",
  doi="10.1137/22M1501040",
  issn="0036-1410",
  url="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001171826200020"
}