Related papers: Distributional Boundary Values: Some New Perspecti…
We obtain new mean value theorems for exponential sums with very smooth numbers, which provide a power saving against the trivial bound in region where previous bounds do not apply.
A piecewise smooth domain is said to have generic corners if the corners are generic CR manifolds. It is shown that a biholomorphic mapping from a piecewise smooth pseudoconvex domain with generic corners in complex Euclidean space that…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic…
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,…
This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such…
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and…
Motivated by applications in materials science, a set of quasiconvexity at the boundary conditions is introduced for domains that are locally diffeomorphic to cones. These conditions are shown to be necessary for strong local minimisers in…
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to this approach is the so-called global relation, which is a…
We prove a Wong-Rosay type theorem for a domain with a piecewise smooth generic strictly pseudoconvex boundary point.
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to…