Search: onr:"swepub:oai:DiVA.org:liu-203044" >
On a new singular a...
On a new singular and degenerate extension of the p-Laplace operator
-
- Baravdish, George, 1964- (author)
- Linköpings universitet,Fysik, elektroteknik och matematik,Tekniska fakulteten
-
- Cheng, Yuanji (author)
- Malmö universitet
-
- Svensson, Olof, 1965- (author)
- Linköpings universitet,Fysik, elektroteknik och matematik,Kommunikations- och transportsystem,Tekniska fakulteten
-
(creator_code:org_t)
- PERGAMON-ELSEVIER SCIENCE LTD, 2024
- 2024
- English.
-
In: Nonlinear Analysis. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0362-546X .- 1873-5215. ; 244
- Related links:
-
https://doi.org/10.1...
-
show more...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
show less...
Abstract
Subject headings
Close
- We study a novel degenerate and singular elliptic operator Δ˜(τ,χ) defined by Δ˜(τ,χ)u=τ(x,Du)(|Du|Δ1u+χ(x,Du)Δ∞u), where the singular weights τ(x,s)>0 and χ(x,s)≥0 are continuous functions on Ω×Rn∖{0}. The operator Δ˜(τ,χ) is an extension of Δ(p,q)u=|Du|qΔ1u+(p−1)|Du|p−2Δ∞u,p≥1,q≥0, introduced by the authors in Baravdishet al. (2020), which in turn is an extension of the p-Laplace operator Δp. We establish the well-posedness of the Neumann boundary value problem for the parabolic equation ut=Δ˜(τ,χ)u in the framework of viscosity solutions. For the solution u, the weight χ controls the evolution along the tangential and the normal directions, respectively, on the level surface of u. The weight τ controls the total speed of the evolution of u. We also prove the consistency and the convergence of the numerical scheme for the finite differences method of the parabolic equation above. Numerical simulations show that our novel nonlinear operator Δ˜(τ,χ) gives better results than both the Perona–Malik (Perona and Malik, 1990) and total variation (TV) methods (Chan and Shen, 2005) when applied to image enhancement.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- p-Laplace operator
- Degenerate singular elliptic operator
- Parabolic equations
- Viscosity solutions
- Image denoising
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
To the university's database