A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method

Alessandro Goffi

doi:10.1007/s40574-022-00340-w

A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method

Alessandro Goffi

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.

Original language	English (US)
Journal	Bolletino dell Unione Matematica Italiana
DOIs	https://doi.org/10.1007/s40574-022-00340-w
State	Published - Nov 5 2022
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-12-07
Acknowledged KAUST grant number(s): CRG2021-4674
Acknowledgements: Open access funding provided by Università degli Studi di Padova within the CRUI-CARE Agreement. The author was partially supported by the INdAM-GNAMPA Project 2022 “Proprietà quantitative e qualitative per EDP non lineari con termini di gradiente” and by the King Abdullah University of Science and Technology (KAUST) project CRG2021-4674 “Mean-Field Games: models, theory and computational aspects". The author wishes to thank Prof. Barles for discussions on gradient estimates via viscosity solutions’ methods and for providing many references on the subject.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1007/s40574-022-00340-w

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title = "A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method",

abstract = "We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.",

author = "Alessandro Goffi",

note = "KAUST Repository Item: Exported on 2022-12-07 Acknowledged KAUST grant number(s): CRG2021-4674 Acknowledgements: Open access funding provided by Universit{\`a} degli Studi di Padova within the CRUI-CARE Agreement. The author was partially supported by the INdAM-GNAMPA Project 2022 “Propriet{\`a} quantitative e qualitative per EDP non lineari con termini di gradiente” and by the King Abdullah University of Science and Technology (KAUST) project CRG2021-4674 “Mean-Field Games: models, theory and computational aspects{"}. The author wishes to thank Prof. Barles for discussions on gradient estimates via viscosity solutions{\textquoteright} methods and for providing many references on the subject. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/s40574-022-00340-w",

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N1 - KAUST Repository Item: Exported on 2022-12-07 Acknowledged KAUST grant number(s): CRG2021-4674 Acknowledgements: Open access funding provided by Università degli Studi di Padova within the CRUI-CARE Agreement. The author was partially supported by the INdAM-GNAMPA Project 2022 “Proprietà quantitative e qualitative per EDP non lineari con termini di gradiente” and by the King Abdullah University of Science and Technology (KAUST) project CRG2021-4674 “Mean-Field Games: models, theory and computational aspects". The author wishes to thank Prof. Barles for discussions on gradient estimates via viscosity solutions’ methods and for providing many references on the subject. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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Y1 - 2022/11/5

N2 - We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.

AB - We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.

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DO - 10.1007/s40574-022-00340-w

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JO - Bolletino dell Unione Matematica Italiana

JF - Bolletino dell Unione Matematica Italiana

ER -

A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method

Abstract

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