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On a family of torsional creep problems in Finsler metrics

Part of: Linear function spaces and their duals Variational principles of physics Existence theories Representations of solutions

Published online by Cambridge University Press:  02 September 2020

Maria Fărcăşeanu ,
Mihai Mihăilescu  and
Denisa Stancu-Dumitru
Maria Fărcăşeanu
Affiliation:
The University of Sydney, Sydney, Australia e-mail: farcaseanu.maria@yahoo.com University Politehnica of Bucharest, Bucharest, Romania e-mail: farcaseanu.maria@yahoo.comdenisa.stancu@yahoo.com
Mihai Mihăilescu*
Affiliation:
University of Craiova, Craiova, Romania
Denisa Stancu-Dumitru
Affiliation:
University Politehnica of Bucharest, Bucharest, Romania e-mail: farcaseanu.maria@yahoo.comdenisa.stancu@yahoo.com
*
e-mail: mmihailes@yahoo.com
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Abstract

The asymptotic behavior of solutions to a family of Dirichlet boundary value problems, involving differential operators in divergence form, on a domain equipped with a Finsler metric is investigated. Solutions are shown to converge uniformly to the distance function to the boundary of the domain, which takes into account the Finsler norm involved in the equation. This implies that a well-known result in the analysis of problems modeling torsional creep continues to hold in this more general setting.

Keywords

Finsler normtorsional creepweak solutiondistance function

MSC classification

Primary: 35D30: Weak solutions 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 49J40: Variational methods including variational inequalities 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49S99: None of the above, but in this section
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 1 , February 2022 , pp. 24 - 41
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

F. M. and D. S-D. have been partially supported by CNCS-UEFISCDI grant no. PN-III-P1-1.1-TE-2019-0456.

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