Detail publikačního výsledku

Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems

BAHROUNI, A.; MISSAOUI, H.; OUNAIES, H.; RADULESCU, V.

Originální název

Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems

Anglický název

Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems

Druh

Článek WoS

Originální abstrakt

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).

Anglický abstrakt

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).

Klíčová slova

ELLIPTIC-EQUATIONS; MULTIPLICITY; REGULARITY; EXISTENCE

Klíčová slova v angličtině

ELLIPTIC-EQUATIONS; MULTIPLICITY; REGULARITY; EXISTENCE

Autoři

BAHROUNI, A.; MISSAOUI, H.; OUNAIES, H.; RADULESCU, V.

Vydáno

21.07.2025

ISSN

0025-2611

Periodikum

MANUSCRIPTA MATHEMATICA

Svazek

176

Číslo

52

Stát

Spolková republika Německo

Strany počet

27

URL

https://link.springer.com/article/10.1007/s00229-025-01652-9

BibTex

@article{BUT198448,
  author="Anouar {Bahrouni} and Hlel {Missaoui} and Hichem {Ounaies} and Vicentiu {Radulescu}",
  title="Orlicz-Sobolev versus Hölder local minimizers for nonlinear Robin problems",
  journal="MANUSCRIPTA MATHEMATICA",
  year="2025",
  volume="176",
  number="52",
  pages="27",
  doi="10.1007/s00229-025-01652-9",
  issn="0025-2611",
  url="https://link.springer.com/article/10.1007/s00229-025-01652-9"
}