Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139545" target="_blank" >RIV/00216224:14310/24:00139545 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00208-023-02764-x" target="_blank" >https://link.springer.com/article/10.1007/s00208-023-02764-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-023-02764-x" target="_blank" >10.1007/s00208-023-02764-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

Popis výsledku v původním jazyce

We study boundary value problems with measure data in smooth bounded domains Omega, for semilinear equations. Specifically we consider problems of the form - L(V)u + f (u) = tau in Omega and tr(V)u = nu on partial derivative Omega, where L-V = Delta + V, f. is an element of C(R) is monotone increasingwith f (0) = 0 and tr V u denotes themeasure boundary trace of u associated with L-V. The potential V is an element of C-1(Omega) typically blows up at a set F subset of partial derivative Omega as dist (x, F)(-2). In general the above boundary value problem may not have a solution. We are interested in questions related to the concept of 'reduced measures', introduced in Brezis et al. (Ann Math Stud 163:55-109, 20072007) for V = 0. Our results extend results of [4] and Brezis and Ponce (J Funct Anal 229(1):95-120, 2005) and apply to a larger class of nonlinear terms f. In the case of signed measures, some of the present results are new even for V = 0.

Název v anglickém jazyce

Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

Popis výsledku anglicky

We study boundary value problems with measure data in smooth bounded domains Omega, for semilinear equations. Specifically we consider problems of the form - L(V)u + f (u) = tau in Omega and tr(V)u = nu on partial derivative Omega, where L-V = Delta + V, f. is an element of C(R) is monotone increasingwith f (0) = 0 and tr V u denotes themeasure boundary trace of u associated with L-V. The potential V is an element of C-1(Omega) typically blows up at a set F subset of partial derivative Omega as dist (x, F)(-2). In general the above boundary value problem may not have a solution. We are interested in questions related to the concept of 'reduced measures', introduced in Brezis et al. (Ann Math Stud 163:55-109, 20072007) for V = 0. Our results extend results of [4] and Brezis and Ponce (J Funct Anal 229(1):95-120, 2005) and apply to a larger class of nonlinear terms f. In the case of signed measures, some of the present results are new even for V = 0.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-17403S" target="_blank" >GA22-17403S: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Svazek periodika

390

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

29

Strana od-do

351-379

Kód UT WoS článku

001118338300001

EID výsledku v databázi Scopus

2-s2.0-85178222888