Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0198448" target="_blank" >RIV/00216305:26220/26:0198448 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00229-025-01652-9" target="_blank" >https://link.springer.com/article/10.1007/s00229-025-01652-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00229-025-01652-9" target="_blank" >10.1007/s00229-025-01652-9</a>

Result language
angličtina
Original language name
Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems
Original language description
We establish regularity results for weak solutions of Robin problems driven by the well-known Orlicz g-Laplacian operator given by (Formula presented.) where Δgu:=div(a(|∇u|)∇u), Ω⊂RN,N≥3, is a bounded domain with C2-boundary ∂Ω, ∂udν=∇u·ν, ν is the unit exterior vector on ∂Ω, p>0, b∈C1,θ(∂Ω) with θ∈(0,1) and infx∈∂Ωb(x)>0. Specifically, using a suitable variation of the Moser iteration technique, we prove that every weak solution of the problem (P) is bounded. Moreover, we combine this result with the Lieberman regularity theorem, to show that every C1(Ω¯)-local minimizer is also a W1,G(Ω)-local minimizer for the corresponding energy functional of problem (P).
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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