Related papers: Regularity for variational problems in the Heisenb…
Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies…
We investigate the maximal $L_p$-regularity in J.L. Lions' problem involving a time-fractional derivative and a non-autonomous form $a(t;\cdot,\cdot)$ on a Hilbert space $H$. This problem says whether the maximal $L_p$-regularity in $H$…
We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact…
We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems arise from variational problems in plasticity with power…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
We consider the problem of minimising the $L^\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$ norm of a function of the gradient and the map itself. We assume zeroth and…
We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard $(p,q)$-growth satisfying the dimension-independent restriction $q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p \leq N-1$,…
Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in \cite{MPSC1}, we study the convergence of minima, minimizers…
We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…
In this paper we study some local and global regularity properties of Fourier series obtained as fractional integrals of modular forms. In particular we characterize the differentiability at rational points, determine their H\"older…
We prove the existence of a continuous $BV$ minimizer with $C^{0}$ boundary value for the $p$-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from $BV$…
The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous…
The purpose of this paper is to study the existence of weak solutions for some classes of one-parameter subelliptic gradient-type systems involving a Sobolev-Hardy potential defined on an unbounded domain $\Omega_\psi$ of the Heisenberg…
We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized $\alpha$-divergences, the…
We revisit the partial $\mathrm{C}^{1,\alpha}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the H\"older exponent $\alpha$ on structural assumptions for general zero-order terms. A…
Local H\"older regularity is established for certain weak solutions to a class of parabolic fractional $p$-Laplace equations with merely measurable kernels. The proof uses DeGiorgi's iteration and refines DiBenedetto's intrinsic scaling…
We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem $$\min_{\mathcal{M}}\frac{1}{2}\int_{\mathcal{M}}|\nabla_{\mathcal{M}}H|^2\,dA$$ where $\mathcal{M}$…
We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions…
We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible…