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Maximal and minimal solutions of second order elliptic and parabolic equations in non-divergence form with measurable coefficients


Authors: M. Cristina Cerutti and Anna Piro Grimaldi
Journal: Proc. Amer. Math. Soc. 145 (2017), 4773-4782
MSC (2010): Primary 35J15, 35J25, 35K10, 35K20
DOI: https://doi.org/10.1090/proc/13577
Published electronically: August 1, 2017
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Abstract: In this paper we will prove that the supremum and infimum of good solutions of the Dirichlet problem for elliptic and parabolic equations in non-divergence form with measurable coefficients, are good solutions to the same problem.


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M. Cristina Cerutti
Affiliation: Dipartimento di Matematica - Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano-Italy
Email: cristina.cerutti@polimi.it

Anna Piro Grimaldi
Affiliation: Dipartimento di Matematica dell’Università di Cagliari, Viale Merello, 94, 09100 Cagliari-Italy
Email: grimaldi@unica.it

DOI: https://doi.org/10.1090/proc/13577
Received by editor(s): May 20, 2009
Received by editor(s) in revised form: November 4, 2016
Published electronically: August 1, 2017
Communicated by: Tatiana Toro
Article copyright: © Copyright 2017 American Mathematical Society

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