Related papers: Asymptotically quasiconvex functionals with genera…

We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials $(\phi_n)_{n=1}^\infty$ on a topologically mixing subshift of finite type $X$ endowed itself with a metric associated…

We study the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set $E$ are defined as $F = \varphi_1(E)$, where $\{ \varphi_t \}$ is a one parameter family of…

In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…

We prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along the imaginary axis, and the elliptic variable $z$ is unrestricted in the complex plane.…

We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } \Omega, \] where $A:\Omega \times \mathbb R^n \to \mathbb R^n$ satisfies a quasi-isotropic $(p,q)$-growth condition, which is…

If the smooth vector fields $X_1,\ldots,X_m$ and their commutators span the tangent space at every point in $\Omega\subseteq \mathbb{R}^N$ for any fixed $m\leq N$, then we establish the full interior regularity theory of quasi-linear…

We prove that minimizers of variational integrals $$ \mathcal E(v)=\int_\Omega f(v)\quad\text{for }v\in\mathcal M(\Omega)\text{ such that } \mathscr{A} v=0, $$ are partially continuous provided that the integrands $f$ are strongly…

We prove global $W^{1,q}(\Omega,\mathbb{R}^m)$-regularity for minimisers of convex functionals of the form $\mathscr{F}(u)=\int_\Omega F(x,Du)\mathrm{d} x$. $W^{1,q}(\Omega,\mathbb{R}^m)$ regularity is also proven for minimisers of the…

We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…

We relate the uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth to the existence of a harmonic function asymptotic to a Busemann function. Parallel to the work of Colding--Minicozzi in the…

We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \mathfrak{F}(v,\Omega) = \int_{\Omega} /! F(Dv(x)) \, dx $$ over $W^{1,p}$--Sobolev mappings $u \colon \Omega \subset {\mathbb…

We consider autonomous integral functionals of the form $\mathcal F[u]:=\int_\Omega f(D u)\,dx$ with $u:\Omega\to\mathbb R^N$ $N\geq1$, where the convex integrand $f$ satisfies controlled $(p,q)$-growth conditions. We establish higher…

Let F be nonnegative, convex and smooth off a compact set K. We prove that continuous local minimisers of convex functionals are "very weak" viscosity solutions in the sense of Juutinen-Lindqvist of the highly singular Euler-Lagrange PDE…

In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms. In particular, the equations with quadratic growth (called natural growth) in the gradient are…

We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed Hankel--Lipschitz space defined via a generalised modulus of continuity. The established results are similar in nature to the…

We establish partial regularity of BD-minima for variational integrals of linear growth which depend on the symmetric gradients and satisfy a weak ellipticity condition. Since there is no Korn Inequality in the $L^{1}$-Setup, the result…

We establish interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, without imposing any restriction on the gap between the highest and lowest growth exponents. Our proof is based on an…

Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally H\"older…

We prove an $\varepsilon$-regularity theorem for $BV^\mathcal{B}$ minimizers of strongly $\mathcal{B}$-quasiconvex functionals with linear growth, where $\mathcal{B}$ is an elliptic operator of the first order. This generalises to the…

Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…