Results 11 to 20 of about 19,228,694 (296)
Weak perturbations of the p-Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2014 We consider the p-Laplacian in R^d perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p>d and p=d and discuss the connection with Sobolev ...
Ekholm, Tomas +2 more
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On Coron's problem for the p-Laplacian [PDF]
Journal of Mathematical Analysis and Applications, 2014 We prove that the critical problem for the $p$-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole.
Mercuri, Carlo +2 more
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INEQUALITIES FOR EIGENFUNCTIONS OF THE P-LAPLACIAN [PDF]
Проблемы анализа, 2013 Motivated by the work of P. Lindqvist, we study eigenfunctions of the one-dimensional p-Laplace operator, the sinp functions, and prove several inequalities for these and p-analogues of other trigonometric functions and their inverse functions.
VUORINEN M, BHAYO B. A
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Solving the $p$-Laplacian on manifolds [PDF]
Proceedings of the American Mathematical Society, 1999 Summary: We prove that the equation \(\Delta_{p}u+h=0\) on a \(p\)-hyperbolic manifold \(M\) has a solution with \(p\)-integrable gradient for any bounded measurable function \(h : M \to \mathbb R\) with compact support.
Marc Troyanov
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A Concentration Phenomenon for p-Laplacian Equation [PDF]
Journal of Applied Mathematics, 2014 It is proved that if the bounded function of coefficient Qn in the following equation -div {|∇u|p-2∇u}+V(x)|u|p-2u=Qn(x)|u|q-2u, u(x)=0 as x∈∂Ω. u(x)⟶0 as |x|⟶∞ is positive in a region contained in Ω and negative outside the region, the sets {Qn ...
Yansheng Zhong
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The Beginning of the Fučik Spectrum for the p-Laplacian
Journal of Differential Equations, 1999 Let \(\Omega\) be a bounded domain in \(\mathbb{R}^N\), \(N\geq 1\) and let \(p\) be a real number greater than \(1\). The Fučik spectrum of the \(p\)-Laplacian \(\Delta_p=\operatorname {div}(|\nabla u|^{p-2}\nabla u)\) on \(W^{1,p}_0(\Omega)\) is defined as the set \(\Sigma_p\) of pairs \((\alpha,\beta)\in \mathbb{R}^2\) such that the Dirichlet ...
Mabel Cuesta +2 more
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Introducing the p-Laplacian spectra [PDF]
Signal Processing, 2020 In this work we develop a nonlinear decomposition, associated with nonlinear eigenfunctions of the p-Laplacian for p \in (1, 2). With this decomposition we can process signals of different degrees of smoothness. We first analyze solutions of scale spaces, generated by -homogeneous operators, \in R. An analytic solution is formulated when the scale
Ido Cohen, Guy Gilboa
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, 2021 A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives.
M. Matar +5 more
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Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas [PDF]
arXiv.org, 2020 We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator.
F. Teso +2 more
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, 2023 We generalise the dynamic Laplacian introduced in (Froyland, 2015) to a dynamic $p$-Laplacian, in analogy to the generalisation of the standard $2$-Laplacian to the standard $p$-Laplacian for $p>1$. Spectral properties of the dynamic Laplacian are connected to the geometric problem of finding "coherent" sets with persistently small boundaries under ...
de Diego Unanue, Alvaro +3 more
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