Related papers: Stability of elliptic Harnack inequality

We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties of holomorphic motions over almost…

We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to…

In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

We prove a version of differential Harnack inequality for a family of sub-elliptic diffusions on Sasakian manifolds under certain curvature conditions.

We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.

We prove that the solvability of the regularity problem in $L^q(\partial \Omega)$ is stable under Carleson perturbations. If the perturbation is small, then the solvability is preserved in the same $L^q$, and if the perturbation is large,…

In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in…

A maniplex of rank n s an n-valent properly edge-coloured graph that generalises, simultaneously, maps on surfaces and abstract polytopes. The problem of stability in maniplexes is a natural variant of the problem of stability in graphs. A…

We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.

We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the…

We introduce minimally expansive and GH-stable points for homeomorphisms on metric spaces and $\mu$-uniformly expansive, $\mu$-shadowable and strong $\mu$-topologically stable points for Borel measures (with respect to a homeomorphism on a…

We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower…

In this paper, we prove that the large energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation.

Our main result gives an improved bound on the filling areas of closed curves in Banach spaces which are not closed geodesics. As applications we show rigidity of Pu's classical systolic inequality and investigate the isoperimetric…

Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E.…

We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.

We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the…

We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.