Results 41 to 50 of about 2,362 (222)
Overdetermined problems with fractional laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 Added a missing assumption (1.3) in Theorem 1.1 and Theorem 1.2, which is used in the proof of Lemma 4 ...
Fall, Mouhamed Moustapha, Jarohs, Sven
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The parabolic p-Laplacian with fractional differentiability [PDF]
IMA Journal of Numerical Analysis, 2020 Abstract We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space–time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiǐ spaces and therefore cover situations when the (gradient of the) solution has only fractional ...
Breit, Dominic +3 more
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Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials
Advanced Nonlinear Studies, 2017 In this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions.
Tang Zhongwei, Wang Lushun
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On the Laplacian and fractional Laplacian in an exterior domain
Advances in Differential Equations, 2012 We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E.
Kosloff, Leonardo, Schonbek, Tomas
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A note on the existence and multiplicity of solutions for sublinear fractional problems
Boundary Value Problems, 2017 In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u ...
Yongqiang Fu
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Critical Concave Convex Ambrosetti–Prodi Type Problems for Fractional 𝑝-Laplacian
Advanced Nonlinear Studies, 2020 In this paper, we consider a class of critical concave convex Ambrosetti–Prodi type problems involving the fractional p-Laplacian operator. By applying the linking theorem and the mountain pass theorem as well, the interaction of the nonlinearities with ...
Bueno H. P. +3 more
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Maximum Principles for Laplacian and Fractional Laplacian with Critical Integrability
The Journal of Geometric Analysis, 2023 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider the critical cases for Laplacian with zero order term and first order term. It is well known that for the Laplacian with zero order term $-Δ+c(x)$ in $B_1$, $c(x)\in L^p(B_1)$($B_1\subset \mathbf{R}^n$), the critical case for
Congming Li, Yingshu Lü
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IEEE Access, 2019 Hadamard fractional calculus theory has made many scholars enthusiastic and excited because of its special logarithmic function integral kernel. In this paper, we focus on a class of Caputo-Hadamard-type fractional turbulent flow model involving $p(t)$ -
Guotao Wang +3 more
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The trace fractional Laplacian and the mid-range fractional Laplacian
Nonlinear AnalysisIn this paper we introduce two new fractional versions of the Laplacian. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian. The second one comes from looking at the classical fractional Laplacian as the mean value (in the sphere) of the 1-dimensional fractional Laplacians in ...
Julio D. Rossi, Jorge Ruiz-Cases
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Advanced Science, EarlyView.Prolonged exposure to stiff extracellular matrix drives cancer‐associated fibroblasts into a persistently activated myofibroblast state. Two parallel pathways are identified: β1 integrin activation smoothens the nuclear lamina to reduce lamin–chromatin contacts, while the formin mDia2 regulates nuclear actin to alter chromatin organization.
Swathi Packirisamy +4 more
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