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.
Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
Maddalena, F.;Solimini, S.
2001-01-01
Abstract
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.File in questo prodotto:
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