Semilinear elliptic equations with Hardy potential and gradient
nonlinearity

J 2020

Semilinear elliptic equations with Hardy potential and gradient nonlinearity

GKIKAS, Konstantinos a Phuoc Tai NGUYEN

Základní údaje

Originální název

Semilinear elliptic equations with Hardy potential and gradient nonlinearity

Autoři

GKIKAS, Konstantinos a Phuoc Tai NGUYEN

Vydání

Revista Matematica Iberoamericana, Zurich, European Mathematical Society, 2020, 0213-2230

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.174

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/20:00114498

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Hardy potential; Martin kernel; boundary trace; critical exponent; gradient term; isolated singularities; removable singularities

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 24. 11. 2020 09:48, 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. In this paper, we study positive solutions of the equation ((*)) - L(mu)u + g(vertical bar del u vertical bar) = 0 in Omega), where L-mu = Delta + mu/delta(2), mu is an element of (0, 1/4] and g is a continuous, nondecreasing function on R+. We prove that if g satisfies a singular integral condition, then there exists a unique solution of ((*)) with a prescribed boundary datum v. When g(t) = t(q) with q is an element of (1, 2), we show that equation ((*)) admits a critical exponent q(mu) (depending only on N and mu). In the subcritical case, namely 1 < q < q(mu), we establish some a priori estimates and provide a description of solutions with an isolated singularity on partial derivative Omega. In the supercritical case, i.e., q(mu) <= q < 2, we demonstrate a removability result in terms of Bessel capacities.

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 a Phuoc Tai NGUYEN. Semilinear elliptic equations with Hardy potential and gradient nonlinearity. Revista Matematica Iberoamericana. Zurich: European Mathematical Society, 2020, roč. 36, č. 4, s. 1207-1256. ISSN 0213-2230. Dostupné z: https://doi.org/10.4171/RMI/1164.

@article{1698716,
   author = {Gkikas, Konstantinos and Nguyen, Phuoc Tai},
   article_location = {Zurich},
   article_number = {4},
   doi = {https://doi.org/10.4171/RMI/1164},
   keywords = {Hardy potential; Martin kernel; boundary trace; critical exponent; gradient term; isolated singularities; removable singularities},
   language = {eng},
   issn = {0213-2230},
   journal = {Revista Matematica Iberoamericana},
   title = {Semilinear elliptic equations with Hardy potential and gradient nonlinearity},
   url = {https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1164&p403=1},
   volume = {36},
   year = {2020}
}

TY  - JOUR
ID  - 1698716
AU  - Gkikas, Konstantinos - Nguyen, Phuoc Tai
PY  - 2020
TI  - Semilinear elliptic equations with Hardy potential and gradient nonlinearity
JF  - Revista Matematica Iberoamericana
VL  - 36
IS  - 4
SP  - 1207-1256
EP  - 1207-1256
PB  - European Mathematical Society
SN  - 02132230
KW  - Hardy potential
KW  - Martin kernel
KW  - boundary trace
KW  - critical exponent
KW  - gradient term
KW  - isolated singularities
KW  - removable singularities
UR  - https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1164&p403=1
L2  - https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1164&p403=1
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. In this paper, we study positive solutions of the equation ((*)) - L(mu)u + g(vertical bar del u vertical bar) = 0 in Omega), where L-mu = Delta + mu/delta(2), mu is an element of (0, 1/4] and g is a continuous, nondecreasing function on R+. We prove that if g satisfies a singular integral condition, then there exists a unique solution of ((*)) with a prescribed boundary datum v. When g(t) = t(q) with q is an element of (1, 2), we show that equation ((*)) admits a critical exponent q(mu) (depending only on N and mu). In the subcritical case, namely 1 < q < q(mu), we establish some a priori estimates and provide a description of solutions with an isolated singularity on partial derivative Omega. In the supercritical case, i.e., q(mu) <= q < 2, we demonstrate a removability result in terms of Bessel capacities.
ER  -

GKIKAS, Konstantinos a Phuoc Tai NGUYEN. Semilinear elliptic equations with Hardy potential and gradient nonlinearity. \textit{Revista Matematica Iberoamericana}. Zurich: European Mathematical Society, 2020, roč.~36, č.~4, s.~1207-1256. ISSN~0213-2230. Dostupné z: https://doi.org/10.4171/RMI/1164.

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