Standard

Variational method for elliptic systems with discontinuous nonlinearities. / Pavlenko, V. N.; Potapov, D. K.

в: Sbornik Mathematics, Том 212, № 5, 726-744, 05.2021, стр. 726-744.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Pavlenko, VN & Potapov, DK 2021, 'Variational method for elliptic systems with discontinuous nonlinearities', Sbornik Mathematics, Том. 212, № 5, 726-744, стр. 726-744. https://doi.org/10.1070/sm9401

APA

Pavlenko, V. N., & Potapov, D. K. (2021). Variational method for elliptic systems with discontinuous nonlinearities. Sbornik Mathematics, 212(5), 726-744. [726-744]. https://doi.org/10.1070/sm9401

Vancouver

Pavlenko VN, Potapov DK. Variational method for elliptic systems with discontinuous nonlinearities. Sbornik Mathematics. 2021 Май;212(5):726-744. 726-744. https://doi.org/10.1070/sm9401

Author

Pavlenko, V. N. ; Potapov, D. K. / Variational method for elliptic systems with discontinuous nonlinearities. в: Sbornik Mathematics. 2021 ; Том 212, № 5. стр. 726-744.

BibTeX

@article{c37b760907dd41dc9b393f0f13d644f7,
title = "Variational method for elliptic systems with discontinuous nonlinearities",
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 = "discontinuous nonlinearity, elliptic system, semiregular solution, strong solution, variational method",
author = "Pavlenko, {V. N.} and Potapov, {D. K.}",
note = "Publisher Copyright: {\textcopyright} 2021 Russian Academy of Sciences (DoM) and London Mathematical Society.",
year = "2021",
month = may,
doi = "10.1070/sm9401",
language = "English",
volume = "212",
pages = "726--744",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "5",

}

RIS

TY - JOUR

T1 - Variational method for elliptic systems with discontinuous nonlinearities

AU - Pavlenko, V. N.

AU - Potapov, D. K.

N1 - Publisher Copyright: © 2021 Russian Academy of Sciences (DoM) and London Mathematical Society.

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - discontinuous nonlinearity

KW - elliptic system

KW - semiregular solution

KW - strong solution

KW - variational method

UR - http://www.scopus.com/inward/record.url?scp=85111563214&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b9893de2-35f8-3a1d-9e6a-47153f7238f2/

U2 - 10.1070/sm9401

DO - 10.1070/sm9401

M3 - Article

AN - SCOPUS:85111563214

VL - 212

SP - 726

EP - 744

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 5

M1 - 726-744

ER -

ID: 84642852