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@article{1698716,
author = {Gkikas, Konstantinos and Nguyen, Phuoc Tai},
article_location = {Zurich},
article_number = {4},
doi = {http://dx.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://dx.doi.org/10.4171/RMI/1164.
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