Related papers: Boundary Smoothness conditions for functions in $R…

We establish the theorems that give necessary and sufficient conditions for an arbitrary function defined in the unit disk of complex plane in order to has boundary values along classes of equivalencies of simple curves. Our results…

Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.

We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our…

We prove $L^p$ lower bounds for Coulomb energy for radially symmetric functions in $\dot H^s(\R^3)$ with $\frac 12 <s<\frac{3}{2}$. In case $\frac 12 <s \leq 1$ we show that the lower bounds are sharp.

In this manuscript we investigate the regularization of solutions for the spatially homogeneous Landau equation. For moderately soft potentials, it is shown that weak solutions become smooth instantaneously and stay so over all times, and…

We give conditions on a pair of Banach spaces $X$ and $Y,$ under which each operator from $X$ to $Y,$ whose second adjoint factors compactly through the space $l^p,$ $1\le p\le+\infty$, itself compactly factors through $l^p.$ The conditions…

For a symplectic manifold $M$ let $\{\cdot,\cdot\}$ be the corresponding Poisson bracket. In this note we prove that the functional $(F,G) \mapsto \|\{F,G\}\|_{L^p(M)}$ is lower-semicontinuous with respect to the $C^0$-norm on…

We prove the weighted $L^p$ regularity of the ordinary Bergman and Cauchy-Szeg\H{o} projections on strongly pseudoconvex domains $D$ in $\mathbb{C}^n$ with near minimal smoothness for appropriate generalizations of the $B_p/A_p$ classes. In…

We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.

We find two-sides estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels, modules of Fourier coefficients of which satisfy…

We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.

We give criteria for the existence of geometric smoothings of a proper lci scheme or a DM stack $X$ as well as for a polarized lci scheme $(X,L)$, without assuming that $X$ is reduced. As applications, we give criteria for the smoothability…

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…

We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, to be polynomially convex. Almost all sufficient conditions known to date --- provided the function…

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality,…

The existence of a smooth, nonnegative, compactly supported function with monotone (on the half-line) Fourier transform satisfying two-sided decay bounds is demonstrated.

A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth…

For functions $f(z)=z^p+a_{n+1}z^{p+1}+...$ defined on the open unit disk, the condition $\Re (f'(z)/z^{p-1})>0$ is sufficient for close-to-convexity of $f$. By making use of this result, several sufficient conditions for close-to-convexity…

We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…