Results 31 to 40 of about 43,034 (224)
, 2016 We consider the fractional Laplacian operator $(-\Delta)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a function and ...
Muratori, Matteo
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On the Aleksandrov–Bakelman–Pucci estimate for the infinity Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2012 We prove $L^\infty$ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and $p$-Laplacian, namely \[ - _p^N u=f\qquad\text{for ...
Charro, F +3 more
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AN ANISOTROPIC INFINITY LAPLACIAN OBTAINED AS THE LIMIT OF THE ANISOTROPIC (p, q)-LAPLACIAN [PDF]
Communications in Contemporary Mathematics, 2011 In this work we study the behavior of the solutions to the following Dirichlet problem related to the anisotropic (p, q)-Laplacian operator [Formula: see text] as p, q → ∞. Here Ω ⊂ ℝN× ℝKand [Formula: see text] and [Formula: see text] denote the gradient of u with respect to the first N variables (x variables) and with respect to the last K variables (
Perez-Llanos, Mayte, Rossi, Julio D.
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Multiplicity for a strongly singular quasilinear problem via bifurcation theory
Bulletin of Mathematical Sciences, 2023 A [Formula: see text]-Laplacian elliptic problem in the presence of both strongly singular and [Formula: see text]-superlinear nonlinearities is considered.
Jacques Giacomoni +2 more
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Weak Comparison Principle for Weighted Fractional p-Laplacian Equation
Journal of Function Spaces, 2020 The aim of this paper is to establish a weak comparison principle for a class fractional p-Laplacian equation with weight. The nonlinear term fx,s>0 is a Carathéodory function which is possibly unbounded both at the origin and at infinity and such that ...
Jin Xie
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Resonant nonlinear periodic problems with the scalar p-Laplacian and a nonsmooth potential [PDF]
, 2006 We study periodic problems driven by the scalar p-Laplacian with a nonsmooth potential. Using the nonsmooth critical point theory for locally Lipsctiz functions,we prove two existence theorems under conditions of resonance at infinity with respect to ...
Aizicovici, Sergiu +2 more
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Advanced Science, EarlyView.Geometry and connectivity are complementary structures, which have demonstrated their ability to represent the brain's functional activity. This study evaluates geometric and connectome eigenmodes as biologically informed constraints for EEG source localization.
Pok Him Siu +6 more
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Advances in Nonlinear Analysis, 2021 In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the origin and at ...
Manouni Said El +2 more
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AIChE Journal, EarlyView.Abstract Generating hydrogel beads pertains to many engineering applications. We examined two alginate‐based fluids at three concentrations of alginate, cAG$$ {c}_{\mathrm{AG}} $$. We used the “Map of Misery” to determine which material property (viscosity, elasticity, and inertia) drives droplet formation.
Conor G. Harris +5 more
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The infinity Laplacian with a transport term
Journal of Mathematical Analysis and Applications, 2013 Abstract We consider the following problem: given a bounded domain Ω ⊂ R n and a vector field ζ : Ω → R n , find a solution to − Δ ∞ u − 〈 D u , ζ 〉 = 0 in Ω , u = f on ∂ Ω , where Δ ∞ is the 1-homogeneous infinity Laplace operator that is formally given by ...
López Soriano, Rafael +2 more
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