Journal title
Archive for Rational Mechanics and Analysis
DOI
10.1007/s00205-017-1113-4
Issue
2
Volume
225
Last updated
2024-04-22T04:32:31.597+01:00
Page
717-769
Abstract
We investigate the properties of certain elliptic systems leading, a~priori,
to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution can in fact be understood as a standard weak solution, with one proviso: analogously as in the case of minimal surface equations, the attainment of the boundary value is penalized by a measure supported on (a subset of) the boundary, which, for the class of problems under consideration here, is the part of the boundary where a Neumann boundary condition is imposed.
to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution can in fact be understood as a standard weak solution, with one proviso: analogously as in the case of minimal surface equations, the attainment of the boundary value is penalized by a measure supported on (a subset of) the boundary, which, for the class of problems under consideration here, is the part of the boundary where a Neumann boundary condition is imposed.
Symplectic ID
589590
Download URL
http://arxiv.org/abs/1601.01907v1
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Publication type
Journal Article
Publication date
18 Apr 2017