Qualitative behavior of axial-symmetric solutions of elliptic free boundary problems.
We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251–277]. As a consequence we get...
We prove an existence result for equations of the form where the coefficients satisfy the usual ellipticity conditions and hypotheses weaker than the continuity with respect to the variable . Moreover, we give a counterexample which shows that the problem above may have no solution if the coefficients are supposed only Borel functions