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On a family of fully
nonlinear integrodifferential operators: from fractional
Laplacian to nonlocal Monge–Ampère
Luis A. Caffarelli and María Soria-Carro |
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Vol. 17 (2024), No. 1, 243–279
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Abstract |
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We introduce a new family of intermediate operators between the fractional Laplacian and the nonlocal Monge–Ampère introduced by Caffarelli and Silvestre that are given by infimums of integrodifferential operators. Using rearrangement techniques, we obtain representation formulas and give a connection to optimal transport. Finally, we consider a global Poisson problem prescribing data at infinity, and prove existence, uniqueness, and -regularity of solutions in the full space. |
Keywords
nonlinear elliptic equations, integrodifferential
operators, fractional Laplacian, Monge–Ampère,
rearrangements
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Mathematical Subject Classification
Primary: 35J60
Secondary: 35B65, 35J96
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Milestones
Received: 1 December 2021
Revised: 5 May 2022
Accepted: 16 June 2022
Published: 5 February 2024
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Authors |
| Luis A. Caffarelli | |
| Department of Mathematics The University of Texas at Austin Austin, TX United States |
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| María Soria-Carro | |
| Department of Mathematics Rutgers University Piscataway, NJ United States |
Department of Mathematics The University of Texas at Austin Austin, TX United States |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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