Very large solutions for the fractional Laplacian: Towards a fractional Keller–Osserman condition
Advances in Nonlinear Analysis, 2017 We look for solutions of (-△)su+f(u)=0{{\left(-\triangle\right)}^{s}u+f(u)=0} in a bounded smooth domain Ω, s∈(0,1){s\in(0,1)}, with a strong singularity at the boundary. In particular, we are interested in solutions which are L1(Ω){L^{1}(\Omega)} and
Abatangelo Nicola
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On the fractional p-Laplacian equations with weight and general datum
Advances in Nonlinear Analysis, 2016 The aim of this paper is to study the following problem:
Abdellaoui Boumediene +2 more
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Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications [PDF]
, 2018 We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
Antil, Harbir, Rautenberg, Carlos N.
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Kirchhoff–Hardy Fractional Problems with Lack of Compactness
Advanced Nonlinear Studies, 2017 This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical ...
Fiscella Alessio, Pucci Patrizia
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Existence Results for a critical fractional equation
, 2016 We are concerned with existence results for a critical problem of Brezis-Nirenberg Type involving an integro-differential operator. Our study includes the fractional Laplacian. Our approach still applies when adding small singular terms.
Bisci, Giovanni Molica +2 more
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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity [PDF]
, 2014 This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical nonlinearity.
Autuori, Giuseppina +2 more
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Generalised Fractional Evolution Equations of Caputo Type [PDF]
, 2017 This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the ...
Hernández-Hernández, M. E. +2 more
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Isoperimetric inequalities for some integral operators arising in potential theory [PDF]
, 2017 In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a ...
EM Harrell +21 more
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Elliptic Pre-Complexes, Hodge-like Decompositions and Overdetermined Boundary-Value Problems
Forum of Mathematics, SigmaWe solve a problem posed by Calabi more than 60 years ago, known as the Saint-Venant compatibility problem: Given a compact Riemannian manifold, generally with boundary, find a compatibility operator for Lie derivatives of the metric tensor. This problem
Raz Kupferman, Roee Leder
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Sequences of weak solutions for fractional equations [PDF]
, 2013 This work is devoted to study the existence of infinitely many weak solutions to nonlocal equations involving a general integrodifferential operator of fractional type.
Bisci, Giovanni Molica
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