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 / Lops, F. A.; Maddalena, F.; Solimini, S.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 18:6(2001), pp. 639-673. [10.1016/S0294-1449(01)00077-4]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
