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Sbornik: Mathematics, 2021, Volume 212, Issue 5, Pages 726–744
DOI: https://doi.org/10.1070/SM9401 (Mi sm9401) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Variational method for elliptic systems with discontinuous nonlinearities

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University, Chelyabinsk, Russia
b Saint Petersburg State University, St. Petersburg, Russia
English version PDF (502 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM9401
Abstract: A system of two elliptic equations with discontinuous nonlinearities and homogeneous Dirichlet boundary conditions is studied. Existence theorems for strong and semiregular solutions are deduced using a variational method. A strong solution is called semiregular if the set on which the values of the solution are points of discontinuity of the nonlinearity with respect to the phase variable has measure zero. Classes of nonlinearities are distinguished for which the assumptions of the theorems established here hold. The variational approach in this paper is based on the concept of a quasipotential operator, by contrast with the traditional approach, which uses the generalized Clark gradient.
Bibliography: 22 titles.
Keywords: elliptic system, discontinuous nonlinearity, strong solution, semiregular solution, variational method.
Received: 01.03.2020 and 22.09.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 5, Pages 133–152
DOI: https://doi.org/10.4213/sm9401
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
PACS: N/A
MSC: Primary 35J50; Secondary 35J60
Language: English
Original paper language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Variational method for elliptic systems with discontinuous nonlinearities”, Mat. Sb., 212:5 (2021), 133–152; Sb. Math., 212:5 (2021), 726–744
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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