Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114435" target="_blank" >RIV/00216224:14310/20:00114435 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/ans-2020-2073" target="_blank" >https://doi.org/10.1515/ans-2020-2073</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ans-2020-2073" target="_blank" >10.1515/ans-2020-2073</a>

Result language
angličtina
Original language name
Elliptic Equations with Hardy Potential and Gradient-Dependent 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. 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).
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
—
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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