Martin kernel of Schrödinger operators with singular potentials and applications to B.V.P. for linear elliptic equations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00119376" target="_blank" >RIV/00216224:14310/22:00119376 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s00526-021-02102-6" target="_blank" >https://link.springer.com/article/10.1007/s00526-021-02102-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-021-02102-6" target="_blank" >10.1007/s00526-021-02102-6</a>

Result language

angličtina

Original language name

Martin kernel of Schrödinger operators with singular potentials and applications to B.V.P. for linear elliptic equations

Original language description

Let (Omega subset {mathbb {R}}^N) ((N ge 3)) be a (C^2) bounded domain and (Sigma subset Omega ) be a compact, (C^2) submanifold in ({mathbb {R}}^N) without boundary, of dimension k with (0le k &lt; N-2). Denote (d_Sigma (x): = mathrm {dist},(x,Sigma )) and (L_mu : = Delta + mu d_Sigma ^{-2}) in (Omega {setminus } Sigma ), (mu in {mathbb {R}}). The optimal Hardy constant (H:=(N-k-2)/2) is deeply involved in the study of the Schrödinger operator (L_mu ). The Green kernel and Martin kernel of (-L_mu ) play an important role in the study of boundary value problems for nonhomogeneous linear equations involving (-L_mu ). If (mu le H^2) and the first eigenvalue of (-L_mu ) is positive then the existence of the Green kernel of (-L_mu ) is guaranteed by the existence of the associated heat kernel. In this paper, we construct the Martin kernel of (-L_mu ) and prove the Representation theory which ensures that any positive solution of the linear equation (-L_mu u = 0) in (Omega {setminus } Sigma ) can be uniquely represented via this kernel. We also establish sharp, two-sided estimates for Green kernel and Martin kernel of (-L_mu ). We combine these results to derive the existence, uniqueness and a priori estimates of the solution to boundary value problems with measures for nonhomogeneous linear equations associated to (-L_mu ).

Czech name

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Czech description

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Type

J_imp - 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

2022

Confidentiality

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

Name of the periodical

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

e-ISSN

1432-0835

Volume of the periodical

61

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

36

Pages from-to

1-36

UT code for WoS article

000717551300005

EID of the result in the Scopus database

2-s2.0-85119156947