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Continuity properties on p for p-Laplacian parabolic problems
(Pergamon-Elsevier B.V. Ltd, 2010-02-01)
In this work we obtain some continuity properties on the parameter p at p = 2 for the Takeuchi-Yamada problem which is a degenerate p-Laplacian version of the Chafee-Infante problem. We prove the continuity of the flows ...
The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
(Springer Heidelberg, 2016-10)
In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ ...
Laplacian coordinates: Theory and methods for seeded image segmentation
(2021-08-01)
Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated ...
Global bifurcation for fractional p-Laplacian and an application
(Heldermann Verlag, 2016-04)
We prove the existence of an unbounded branch of solutions to the nonlinear non-local equation (Equation presented) bifurcating from the first eigenvalue. Here (-Δ)s p denotes the fractional p-Laplacian and Ω ⊂ ℝ1 is a ...
Limits as p(x) → ∞ of p(x)-harmonic functions
(Elsevier, 2010-01)
In this note we study the limit as p(x) → ∞ of solutions to −∆p(x)u = 0 in a domain Ω, with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +∞ and ...
Clustering for metric graphs using the p-Laplacian
(Michigan Mathematical Journal, 2016-08)
We deal with the clustering problem in a metric graph. We look for two clusters, and to this end, we study the first nonzero eigenvalue of the p Laplacian on a quantum graph with Newmann or Kirchoff boundary conditions on ...
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian
(Academic Press Inc Elsevier Science, 2017-03-03)
Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of (−Δp)su=c(x)|u|p−2u in Ω where Ω is an open set of RN, s∈(0,1), p∈(1,+∞), c∈C(Ω‾) and (−Δp)s is the fractional p-Laplacian.
Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
(Univ Szeged, 2017-11)
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...
Exponential stability for a plate equation with p-Laplacian and memory terms
(WILEY-BLACKWELLMALDEN, 2012)
This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary ...
Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian
(Springer, 2017-03)
In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the ...