Energy approximation for some double phase functionals
In the present manuscript we give a structure condition that allows for energy approximation in the vectorial case and we provide two examples, enjoying such a condition.
math.AP↗
arXiv subjects
Menita Carozza
Publications and source records attributed to Menita Carozza.
Quasiconvex Bulk and Surface Energies with subquadratic growth
We establish partial Hölder continuity of the gradient for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The bulk energy densities are uniformly strictly quasiconvex functions with $p$-growth, $1<p< 2$, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand $Φ$ not necessarily regular.
math.OC↗
Continuity properties of weakly monotone Orlicz-Sobolev functions
The notion of weakly monotone functions extends the classical definition of monotone function, that can be traced back to H.Lebesgue. It was introduced, in the setting of Sobolev spaces, by J.Manfredi, and thoroughly investigated in the more general framework of Orlicz-Sobolev spaces by diverse authors, including T.Iwaniec, J.Kauhanen, P.Koskela, J.Maly, J.Onninen, X.Zhong. The present paper complements and augments the available theory of pointwise regularity properties of weakly monotone functions in Orlicz-Sobolev spaces. In particular, a variant is proposed in a customary condition ensuring the continuity of functions from these spaces which avoids a technical additional assumption, and applies to certain situations when the latter is not fulfilled. The continuity outside sets of zero Orlicz capacity, and outside sets of (generalized) zero Hausdorff measure, will are also established when everywhere continuity fails.
math.FA↗
Regularity Results for an Optimal Design Problem with a Volume Constraint
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u;E), Hoelder continuity of the function u is proved as well as partial regularity of the boundary of the minimal set E. Moreover, full regularity of the boundary of the minimal set is obtained under suitable closeness assumptions on the eigenvalues of the bulk energies.
math.AP↗
Regularity of minimizers of autonomous convex variational integrals
We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \mathfrak{F}(v,Ω) = \int_Ω /! F(Dv(x)) \, dx $$ over $W^{1,p}$--Sobolev mappings $u \colon Ω\subset {\mathbb R}^n \to {\mathbb R}^N$ satisfying a Dirichlet boundary condition. The integrands $F$ are assumed to be autonomous, convex and of $(p,q)$ growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range $1<p \leq q < p^{\ast}$, where $p^{\ast}$ denotes the Sobolev conjugate exponent of $p$.
math.AP↗