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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair


IMPACT FACTOR 2018: 1.650

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2169-0375
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Volume 16, Issue 2

Issues

Obstacle Problems and Maximal Operators

Pablo Blanc
  • Departmento de Mathematica, FCEyN, Buenos Aires University, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
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/ Juan P. Pinasco
  • Departmento de Mathematica, FCEyN, Buenos Aires University, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
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/ Julio D. Rossi
  • Corresponding author
  • Departmento de Mathematica, FCEyN, Buenos Aires University, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
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Published Online: 2016-04-13 | DOI: https://doi.org/10.1515/ans-2015-5044

Abstract

Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li (i=1,2 alternating them) with obstacle given by the previous term un-1 in a domain Ω and a fixed boundary datum g on Ω. We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L1u,L2u}=0 in Ω with u=g on Ω.

Keywords: Dirichlet Boundary Conditions; Obstacle Problems; Maximal Operators

MSC 2010: 35J70; 49N70; 91A15; 91A24

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About the article

Received: 2015-07-08

Revised: 2015-08-18

Accepted: 2015-08-19

Published Online: 2016-04-13

Published in Print: 2016-05-01


Citation Information: Advanced Nonlinear Studies, Volume 16, Issue 2, Pages 355–362, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2015-5044.

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