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@article{1689997,
author = {Gkikas, Konstantinos T. and Nguyen, Phuoc Tai},
article_location = {Berlin},
article_number = {2},
doi = {http://dx.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://dx.doi.org/10.1515/ans-2020-2073.
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