On the existence of integrable solutions to nonlinear elliptic systems and variational problems with linear growth
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Archive for Rational Mechanics and Analysis |
| Volume: | 225 |
| Number: | 2 |
| Year: | 2017 |
| Pages: | 717--769 |
| URL: | https://arxiv.org/abs/1601.019... |
| DOI: | 10.1007/s00205-017-1113-4 |
| 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. |
| Preprint project: | MORE |
| Preprint year: | 2016 |
| Preprint number: | 01 |
| Preprint ID: | MORE/2016/01 |
| Keywords: | |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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