Abstract
We study the pointwise convergence and the Γ-convergence of a family of non-local, non-convex functionals Λδ in Lp(Ω) for p>1. We show that the limits are multiples of ∫Ω|∇u|p. This is a continuation of our previous work where the case p=1 was considered.
Original language | English (US) |
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Article number | 111626 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 191 |
DOIs | |
State | Published - Feb 2020 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Keywords
- Non-convex
- Non-local
- Pointwise convergence
- Sobolev norms
- Γ-convergence