Semilinear elliptic equations with Hardy potential and gradient nonlinearity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114498" target="_blank" >RIV/00216224:14310/20:00114498 - isvavai.cz</a>
Result on the web
<a href="https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1164&p403=1" target="_blank" >https://www.ems-ph.org/journals/of_article.php?jrn=rmi&doi=1164&p403=1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RMI/1164" target="_blank" >10.4171/RMI/1164</a>

Result language
angličtina
Original language name
Semilinear elliptic equations with Hardy potential and gradient nonlinearity
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Linear and nonlinear elliptic equations with singular data and related problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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