Elliptic Equations with Hardy Potential and Gradient-Dependent
Nonlinearity

J 2020

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN

Základní údaje

Originální název

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Autoři

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN

Vydání

Advanced Nonlinear Studies, Berlin, Walter de Gruyter GmbH, 2020, 1536-1365

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.446

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/20:00114435

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Hardy Potential; Singular Solutions; Boundary Trace; Uniqueness; Critical Exponent; Gradient Term; Isolated Singularities

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 11. 2020 16:53, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Let Omega subset of R-N (N >= 3) be a C-2 bounded domain, and let delta be the distance to partial derivative Omega. We study equations (E-+/-), -L(mu)u +/- g(u, vertical bar del u vertical bar) = 0 in Omega, where L-mu = Delta + mu/delta(2), mu epsilon (0, 1/4] and g: R x R+ -> R+ is nondecreasing and locally Lipschitz in its two variables with g(0, 0) = 0. We prove that, under some subcritical growth assumption on g, equation (E+) with boundary condition u = v admits a solution for any nonnegative bounded measure on partial derivative Omega, while equation (E-) with boundary condition u = v admits a solution provided that the total mass of v is small. Then we analyze the model case g(s, t) = vertical bar s vertical bar(p) t(q) and obtain a uniqueness result, which is even new with mu = 0. We also describe isolated singularities of positive solutions to (E+) and establish a removability result in terms of Bessel capacities. Various existence results are obtained for (E-). Finally, we discuss existence, uniqueness and removability results for (E-+/-) in the case g(s, t) = vertical bar s vertical bar(p) + t(q).

Návaznosti

GJ19-14413Y, projekt VaV

Název: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy

Investor: Grantová agentura ČR, Lineární a nelineární eliptické rovnice se singulárními daty a související problémy

Citovat

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN. Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity. Advanced Nonlinear Studies. Berlin: Walter de Gruyter GmbH, 2020, roč. 20, č. 2, s. 399-435. ISSN 1536-1365. Dostupné z: https://doi.org/10.1515/ans-2020-2073.

@article{1689997,
   author = {Gkikas, Konstantinos T. and Nguyen, Phuoc Tai},
   article_location = {Berlin},
   article_number = {2},
   doi = {https://doi.org/10.1515/ans-2020-2073},
   keywords = {Hardy Potential; Singular Solutions; Boundary Trace; Uniqueness; Critical Exponent; Gradient Term; Isolated Singularities},
   language = {eng},
   issn = {1536-1365},
   journal = {Advanced Nonlinear Studies},
   title = {Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity},
   url = {https://doi.org/10.1515/ans-2020-2073},
   volume = {20},
   year = {2020}
}

TY  - JOUR
ID  - 1689997
AU  - Gkikas, Konstantinos T. - Nguyen, Phuoc Tai
PY  - 2020
TI  - Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity
JF  - Advanced Nonlinear Studies
VL  - 20
IS  - 2
SP  - 399-435
EP  - 399-435
PB  - Walter de Gruyter GmbH
SN  - 15361365
KW  - Hardy Potential
KW  - Singular Solutions
KW  - Boundary Trace
KW  - Uniqueness
KW  - Critical Exponent
KW  - Gradient Term
KW  - Isolated Singularities
UR  - https://doi.org/10.1515/ans-2020-2073
L2  - https://doi.org/10.1515/ans-2020-2073
N2  - Let Omega subset of R-N (N >= 3) be a C-2 bounded domain, and let delta be the distance to partial derivative Omega. We study equations (E-+/-), -L(mu)u +/- g(u, vertical bar del u vertical bar) = 0 in Omega, where L-mu = Delta + mu/delta(2), mu epsilon (0, 1/4] and g: R x R+ -> R+ is nondecreasing and locally Lipschitz in its two variables with g(0, 0) = 0. We prove that, under some subcritical growth assumption on g, equation (E+) with boundary condition u = v admits a solution for any nonnegative bounded measure on partial derivative Omega, while equation (E-) with boundary condition u = v admits a solution provided that the total mass of v is small. Then we analyze the model case g(s, t) = vertical bar s vertical bar(p) t(q) and obtain a uniqueness result, which is even new with mu = 0. We also describe isolated singularities of positive solutions to (E+) and establish a removability result in terms of Bessel capacities. Various existence results are obtained for (E-). Finally, we discuss existence, uniqueness and removability results for (E-+/-) in the case g(s, t) = vertical bar s vertical bar(p) + t(q).
ER  -

GKIKAS, Konstantinos T. a Phuoc Tai NGUYEN. Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity. \textit{Advanced Nonlinear Studies}. Berlin: Walter de Gruyter GmbH, 2020, roč.~20, č.~2, s.~399-435. ISSN~1536-1365. Dostupné z: https://doi.org/10.1515/ans-2020-2073.

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