Logarithmic double phase problems with critical growth on the boundary
Abstract
Abstract In this paper, we study logarithmic double phase problems with critical growth on the boundary of the form $$\begin{aligned} -\operatorname {div} {\mathcal {L}}(u)=-|u|^{p-2}u \quad \text {in } \Omega , \quad {\mathcal {L}}(u)\cdot \nu = f(x,u)+ |u|^{p_*-2}u \quad \text {on } \partial \Omega , \end{aligned}$$ - div L ( u ) = - | u | p - 2 u in Ω , L ( u ) · ν = f ( x , u ) + | u | p ∗ - 2 u on ∂ Ω , where $$\operatorname {div} {\mathcal {L}}$$ div L stands for the logarithmic double phase operator given by $$\begin{aligned} \operatorname {div} \left( |\nabla u|^{p-2} \nabla u + \mu (x) \left[ \log (e + |\nabla u|) + \frac{|\nabla u|}{q(e + |\nabla u|)} \right] |\nabla u|^{q-2} \nabla u \right) , \end{aligned}$$ div | ∇ u | p - 2 ∇ u + μ ( x ) log ( e + | ∇ u | ) + | ∇ u | q ( e + | ∇ u | ) | ∇ u |
Fields of Study & Subjects
Meromorphic and Entire Functions
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Journal of Elliptic and Parabolic Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 1
- Pages
- 895–918
- Publication date
- 26 February 2026
- Language
- EN