The paper deals with the problem of minimizing a free discontinuity functional under Dirichlet boundary conditions. An existence result was known so far for C-1 (partial derivative Omega) boundary data u. We show here that the same result holds for (u) over cap epsilon C-0.u(partial derivative Omega) if it > 1/2 and it cannot be extended to cover the case mu = 1/2 The proof is based on some geometric measure theoretic properties, in part introduced here, which are proved a priori to hold for all the possible minimizers.
|Titolo:||Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities|
|Data di pubblicazione:||2001|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/S0294-1449(01)00077-4|
|Appare nelle tipologie:||1.1 Articolo in rivista|