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St. Petersburg Mathematical Journal

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A borderline case of Calderón-Zygmund estimates for nonuniformly elliptic problems


Authors: C. De Filippis and G. Mingione
Original publication: Algebra i Analiz, tom 31 (2019), nomer 3.
Journal: St. Petersburg Math. J. 31 (2020), 455-477
MSC (2010): Primary 35H10; Secondary 35J30
DOI: https://doi.org/10.1090/spmj/1608
Published electronically: April 30, 2020
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Abstract: In a borderline case which was not covered before, nonlinear Calderón-Zygmund estimates are shown to be valid for a class of nonuniformly elliptic problems driven by double phase energies.


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Additional Information

C. De Filippis
Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX26GG, Oxford, United Kingdom
Email: Cristiana.DeFilippis@maths.ox.ac.uk

G. Mingione
Affiliation: Dipartimento SMFI, Università di Parma, Viale delle Scienze 53/a, Campus, 43124 Parma, Italy
Email: giuseppe.mingione@unipr.it

DOI: https://doi.org/10.1090/spmj/1608
Keywords: Calder\'on--Zygmund estimates, nonuniformly elliptic problems, Lavrent{\textprime}ev phenomenon, Euler--Lagrange equations, $p$-Laplacian, homogenization
Received by editor(s): September 26, 2018
Published electronically: April 30, 2020
Additional Notes: This work was supported by the Engineering and Physical Sciences Research Council [EP/L015811/1]
Dedicated: Dedicated to the memory of S. G. Mikhlin
Article copyright: © Copyright 2020 American Mathematical Society