L∞ a-priori estimates for subcritical semilinear elliptic equations with a Carathéodory nonlinearity
dc.contributor.author | Pardo San Gil, Rosa María | |
dc.date.accessioned | 2023-06-22T12:30:17Z | |
dc.date.available | 2023-06-22T12:30:17Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We present new L∞ a priori estimates for weak solutions of a wide class of subcritical elliptic equations in bounded domains. No hypotheses on the sign of the solutions, neither of the non-linearities are required. This method is based in combining elliptic regularity with Gagliardo-Nirenberg or Caffarelli-Kohn-Nirenberg interpolation inequalities. Let us consider a semilinear boundary value problem −Δu=f(x,u), in Ω, with Dirichlet boundary conditions, where Ω⊂RN, with N>2, is a bounded smooth domain, and f is a subcritical Carathéodory non-linearity. We provide L∞ a priori estimates for weak solutions, in terms of their L2∗-norm, where 2∗=2N/N−2 is the critical Sobolev exponent. By a subcritical non-linearity we mean, for instance, |f(x,s)|≤|x|−μ˜f(s), where μ∈(0,2), and ˜f(s)/|s|2∗μ−1→0 as |s|→∞, here 2∗μ:=2(N−μ)/N−2 is the critical Sobolev-Hardy exponent. Our non-linearities includes non-power non-linearities. In particular we prove that when f(x,s)=|x−μ |s|2∗μ−2s/[log(e+|s|)]β, with μ∈[1,2), then, for any ε>0 there exists a constant Cε>0 such that for any solution u∈H10(Ω), the following holds [log(e+∥u∥∞)]β≤Cε(1+∥u∥2∗)(2∗μ−2)(1+ε). | |
dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | FALSE | |
dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
dc.description.sponsorship | Universidad Complutense de Madrid | |
dc.description.status | unpub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/75705 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/72705 | |
dc.language.iso | eng | |
dc.relation.projectID | PID2019-103860GB-I00 | |
dc.relation.projectID | CADEDIF UCM (920894) | |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | |
dc.rights.accessRights | open access | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
dc.subject.cdu | 517.95 | |
dc.subject.keyword | A priori estimates | |
dc.subject.keyword | Subcritical non-linearities | |
dc.subject.keyword | L∞ a priori bounds | |
dc.subject.keyword | Changing sign weights | |
dc.subject.keyword | Singular elliptic equations | |
dc.subject.ucm | Ecuaciones diferenciales | |
dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
dc.title | L∞ a-priori estimates for subcritical semilinear elliptic equations with a Carathéodory nonlinearity | |
dc.type | journal article | |
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dspace.entity.type | Publication | |
relation.isAuthorOfPublication | b61446bc-a011-4f38-9387-63e24d811d3a | |
relation.isAuthorOfPublication.latestForDiscovery | b61446bc-a011-4f38-9387-63e24d811d3a |
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