Papers by Giuseppe Mingione
We present pointwise gradient bounds for solutions to $p$-Laplacean type non-homogeneous equation... more We present pointwise gradient bounds for solutions to $p$-Laplacean type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic equations.
We consider the integral functional R f(x,Du)dx under non stan- dard growth assumptions of (p,q)-... more We consider the integral functional R f(x,Du)dx under non stan- dard growth assumptions of (p,q)-type: namely, we assume that |z|p(x) � f(x,z) � L(1 + |z|p(x)) for some function p(x) > 1, a condition appearing in several models from math- ematical physics. Under sharp assumptions on the continuous function p(x) we prove partial regularity of minimizers in the vector-valued case
We prove regularity results for solutions to a class of quasilinear elliptic equations in diverge... more We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H n . The model case is the nondegenerate p-Laplacean operator
We consider the integral functional f (x, Du) dx under non-standard growth assumptions that we ca... more We consider the integral functional f (x, Du) dx under non-standard growth assumptions that we call p(x) type: namely, we assume that
We prove that, if u : Ω → R N is a solution to the Dirichlet variational problem
Lack of regularity of local minimizers for convex functionals with nonstandard growth conditions ... more Lack of regularity of local minimizers for convex functionals with nonstandard growth conditions is considered. It is shown that for every ε > 0 there exists a function a ∈ C α (Ω) such that the functional
We prove regularity results for weak solutions to systems modelling electrorheological fluids in ... more We prove regularity results for weak solutions to systems modelling electrorheological fluids in the stationary case, as proposed in ; a particular case of the system we consider is
We prove partial regularity for minimizers of quasiconvex functionals of the type Ω f (x, Du) dx ... more We prove partial regularity for minimizers of quasiconvex functionals of the type Ω f (x, Du) dx with p(x) growth with respect to the second variable. The proof is direct and it uses a method of A-harmonic approximation.
We provide bounds for the Hausdorff dimension of the singular set of minima of functionals of the... more We provide bounds for the Hausdorff dimension of the singular set of minima of functionals of the type Ω F (x, v, Dv), where F is only Hölder continuous with respect to the variables (x, v).
Nodea-nonlinear Differential Equations and Applications, 2000
We prove C 1,α -partial regularity of minimizers u ∈ W 1,1 loc (Ω; R N ), with Ω ⊂ R n , for a cl... more We prove C 1,α -partial regularity of minimizers u ∈ W 1,1 loc (Ω; R N ), with Ω ⊂ R n , for a class of convex integral functionals with nearly linear growth whose model is
Higher difi'erentiability for minimizers of irregular integrals
A Remark on C^0,α Regularity of ω-minima
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006
A new model for the energy of a mixture of micromagnetic materials is introduced within the conte... more A new model for the energy of a mixture of micromagnetic materials is introduced within the context of functions with special bounded variation. Existence and regularity for the solution of an optimal design problem in micromagnetics are obtained.
Nonlinear Analysis: Theory, Methods & Applications, 1999
Nonlinear Analysis: Theory, Methods & Applications, 2001
Nonlinear Differential Equations and Applications NoDEA, 2008
We prove partial regularity for minimizers of quasiconvex functionals of the type Ω f (x, Du) dx ... more We prove partial regularity for minimizers of quasiconvex functionals of the type Ω f (x, Du) dx with p(x) growth with respect to the second variable. The proof is direct and it uses a method of A-harmonic approximation.
Nonlinear Differential Equations and Applications, 2000
We prove C 1,α -partial regularity of minimizers u ∈ W 1,1 loc (Ω; R N ), with Ω ⊂ R n , for a cl... more We prove C 1,α -partial regularity of minimizers u ∈ W 1,1 loc (Ω; R N ), with Ω ⊂ R n , for a class of convex integral functionals with nearly linear growth whose model is
Memoirs of the American Mathematical Society, 2011
Mathematische Annalen, 2007
We prove regularity results for solutions to a class of quasilinear elliptic equations in diverge... more We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H n . The model case is the nondegenerate p-Laplacean operator
Journal of Mathematical Analysis and Applications, 2009
We give a survey of known and not known harmonic type approximation lemmas which are descendants ... more We give a survey of known and not known harmonic type approximation lemmas which are descendants of the classical De Giorgi's one, and we outline some of their recent or possible applications.
Uploads
Papers by Giuseppe Mingione