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On a family of inhomogeneous torsional creep problems


Authors: Marian Bocea and Mihai Mihăilescu
Journal: Proc. Amer. Math. Soc. 145 (2017), 4397-4409
MSC (2010): Primary 35D30, 35D40, 46E30, 46E35, 49J40, 49J45, 49S99
DOI: https://doi.org/10.1090/proc/13583
Published electronically: May 4, 2017
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Abstract: The asymptotic behavior of solutions to a family of Dirichlet boundary value problems involving inhomogeneous PDEs in divergence form is studied in an Orlicz-Sobolev setting. Solutions are shown to converge uniformly to the distance function to the boundary of the domain. This implies that a well-known result in the analysis of problems modeling torsional creep continues to hold under much more general constitutive assumptions on the stress.


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Additional Information

Marian Bocea
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, 1032 W. Sheridan Road, Chicago, Illinois 60660
Email: mbocea@luc.edu

Mihai Mihăilescu
Affiliation: Department of Mathematics, University of Craiova, 200585 Craiova, Romania — and — “Simion Stoilow” Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
Email: mmihailes@yahoo.com

DOI: https://doi.org/10.1090/proc/13583
Keywords: Inhomogeneous equations, Orlicz-Sobolev spaces, torsional creep, viscosity solutions
Received by editor(s): April 28, 2016
Received by editor(s) in revised form: November 9, 2016
Published electronically: May 4, 2017
Additional Notes: The research of the first author was partially supported by the U.S. National Science Foundation under Grant No. DMS-1515871. The second author was partially supported by CNCS-UEFISCDI Grant No. PN-III-P4-ID-PCE-2016-0035.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2017 American Mathematical Society