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Variational mean curvatures for general domains
Thomas Schmidt, Jule Helena Schütt
The notion of variational mean curvature (VMC) arises from Massari's variational approach to hypersurfaces of prescribed mean curvature and expresses a minimizing property for Mass…
Existence theory for linear-growth variational integrals with signed measure data
Eleonora Ficola, Thomas Schmidt
We develop a semicontinuity-based existence theory in for a general class of scalar linear-growth variational integrals with additional signed-measure terms. The resu…
Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem
Thomas Schmidt, Jule Helena Schütt
We revisit the partial regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent on structural as…
Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data
Eleonora Ficola, Thomas Schmidt
We study the minimization of anisotropic total variation functionals with additional measure terms among functions of bounded variation subject to a Dirichlet boundary condition. M…