Archive for Rational Mechanics and Analysis

, Volume 225, Issue 2, pp 717–769 | Cite as

On the Existence of Integrable Solutions to Nonlinear Elliptic Systems and Variational Problems with Linear Growth

  • Lisa Beck
  • Miroslav Bulíček
  • Josef Málek
  • Endre Süli
Article

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 radial structure, then the solution can in fact be understood as a standard weak solution, with one proviso: analogously to 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.

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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany
  2. 2.Mathematical Institute, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic
  3. 3.Mathematical InstituteUniversity of OxfordOxfordUK

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