Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Popis výsledku v původním jazyce

Let Omega subset of R-N (N &gt;= 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+ -&gt; 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).

Název v anglickém jazyce

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Popis výsledku anglicky

Let Omega subset of R-N (N &gt;= 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+ -&gt; 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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advanced Nonlinear Studies

ISSN

1536-1365

e-ISSN

2169-0375

Svazek periodika

20

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

37

Strana od-do

399-435

Kód UT WoS článku

000531060200011

EID výsledku v databázi Scopus

2-s2.0-85081408940