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 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 problems under consideration here, is the part of
the boundary where a Neumann boundary condition is imposed. Finally, we
will connect such elliptic systems with certain problems in elasticity theory-
the limiting strain models. |
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