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This paper is on $Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the geometry of the Heisenberg group. Without using special geometric features, these functionals would be neither coercive nor periodic, so classic results do not apply. All the results apply to the more general case of Carnot groups.
We study Gamma-convergence of graph based Ginzburg-Landau functionals, both the limit for zero diffusive interface parameter epsilon->0 and the limit for infinite nodes in the graph m -> infinity. For general graphs we prove that in the limit epsilon
A novel general framework for the study of $Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $Gamma$-limit of these kind of functionals by knowing the $Gamma$-li
In this manuscript we establish local Holder regularity estimates for bounded solutions of a certain class of doubly degenerate evolution PDEs. By making use of intrinsic scaling techniques and geometric tangential methods, we derive sharp regularity
We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-infty, T) times mathbb{R}^d_+$, where $mathbb{R}^d_+ = {x in mathbb{R}^d,:, x_d>0
In this work we give a proof of the mean-field limit for $lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of function