Fractional p-eigenvalues

By Giovanni Franzina, Giampiero Palatucci. 2013

309 citations recorded by the source corpus.

We discuss some basic properties of the eigenfunctions of a class of nonlocal operators whose model is the fractional p-Laplacian.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7d38d571efe6f5581c62f652b9c41ba6280d9c5c

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “The eigenvalue problem for the fractional p-Laplacian and properties like the simplicity of the smallest eigenvalue is studied in [16, 32].”
Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations (2016, background): “For other fractional Caccioppoli-type inequalities, though not taking into account the tail contribution, see [32,33], and also [12].”
Degenerate Kirchhoff-type diffusion problems involving the fractional p-Laplacian (2017, background): “We refer the reader to [7, 14, 22, 39] for further details on fractional Laplacian and the fractional Sobolev spaces.”
Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spaces (2019, background): “In recent years, problem (Pp) has been studied in many papers, we refer to [4,5,26,29], in which the authors have used different methods to get existence of solutions for (Pp).”
Eigenvalues and minimizers for a non-standard growth non-local operator (2018, background): “This line of research was widely continued, only to mention a few works, we remit to [6, 7, 15] and references to these papers.”
Bifurcation and multiplicity results for critical fractional p‐Laplacian problems (2014, background): “In particular, fractional p-eigenvalue problems have been studied in Brasco and Parini [7], Brasco, Parini and Squassina [6], Franzina and Palatucci [19], Iannizzotto and Squassina [26] and in Lindgren and Lindqvist [29].”
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, background): “1 nonlocal case, see Di Nezza-Palatucci-Valdinoci [34], Lindgren-Lindqvist [54], Brasco-LindgrenParini [18], Brasco-Parini [19], Franzina-Palatucci [44], Nguyen-Dı́az-Quoc-Hung [58] and the references therein.”
The second eigenvalue of the fractional p-Laplacian (2014, background): “1) was first introduced by Lindgren and Lindqvist in [21] and investigated by several authors afterwards, we cite for example [4, 14] and [18].”
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators (2021, background): “As for the nonlinear case, the spectral properties of the fractional p-Laplacian possess their own special features, see [34], and they typically combine the difficulties coming from the nonlocal world with those arising from the theory of nonlinear operators.”
The obstacle problem for nonlinear integro-differential operators (2016, background): “For other fractional Caccioppoli-type inequalities, though not taking into account the tail contribution, see [17,31,32].”
The Brezis–Nirenberg problem for the fractional p-Laplacian (2015, background): “[7], Brasco and Parini [6], Franzina and Palatucci [21], Iannizzotto and Squassina [30], and Lindgren and Lindqvist [35].”
Fractional elliptic equations with critical exponential nonlinearity (2016, background): “This contradicts the isolatedness of smallest eigenvalue [10].”
Local behavior of fractional $p$-minimizers (2015, unknown): “See also [9] for some basic results for fractional p-eigenvalues.”
Stability of variational eigenvalues for the fractional p−Laplacian (2015, background): “Many efforts have been devoted to the study of problems involving the fractional p−Laplacian operator, among which we mention eigenvalue problems [7,20,24,29], regularity theory [14,20,25, 27,28] and existence of solutions within the framework of Morse theory [26].”