Related papers: On boundary properties of solutions of complex vec…
The Fourier transform plays a central role in many geometric and combinatorial problems cast in vector spaces over finite fields. If a set admits optimal $L^\infty$ bounds on its Fourier transform (that is, it is a Salem set), then it can…
This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to…
Given a continuous function on the boundary of a bounded open set in $\mathbb{R}^d$ there exists a unique bounded harmonic function, called the Perron solution, taking the prescribed boundary values at least at all regular points (in the…
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities,…
We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…
This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the…
We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary H\"older continuity of the solutions of related Dirichlet problems. Then, we present some applications…
This paper is aimed to investigate the strong $L^p$-closure $L_{\mathbb{Z}}^p(B)$ of the vector fields on the open unit ball $B\subset\mathbb{R}^3$ that are smooth up to finitely many integer point singularities. First, such strong closure…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…
Elliptic estimates in Hardy classes are proved on domains with minimally smooth boundary. The methodology is different from the original methods of Chang/Krantz/Stein.
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
In a smooth bounded domain we obtain existence, uniqueness, regularity and boundary behavior for a class of singular quasi-linear elliptic equations.
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.