Related papers: Concave Toric Domains in Stark-type Mechanical Sys…

We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…

We consider two inverse problems related to the tokamak \textsl{Tore Supra} through the study of the magnetostatic equation for the poloidal flux. The first one deals with the Cauchy issue of recovering in a two dimensional annular domain…

In bounded convex domains, the regularity estimates of a vector field $\u$ with its $\dv\u$, $\curl\u$ in $L^r$ space and the tangential components or the normal component of $\u$ over the boundary in $L^r$ space, are established for…

We give a sharp lower bound on the area of a domain that can be enclosed by a closed embedded $\lambda$-convex curve of a given length on the Lobachevsky plane.

With the aid of the technique of variation of domains developed in Memoirs of Amer. Math. Soc., Vol. 209, No. 984, 2011, we characterize the pseudoconvex domains with smooth boundary in Hopf surfaces which are not Stein.

We construct solution operators to the $\overline{\partial}$-equation that depend continuously on the domain. This is applied to derive a parameter version of Forstneri\v{c}'s splitting lemma: If both the maps and the domains they are…

We develop computer assisted arguments for proving the existence of transverse homoclinic connecting orbits, and apply these arguments for a number of non-perturbative parameter and energy values in the spatial equilateral circular…

We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each…

We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where…

In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing…

Within a theory of the existing fundamental length on the order of Planck's a high-energy deformation of the General Relativity for the space with horizon has been constructed. On this basis, Markov's work of the early eighties of the last…

We exploit the connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating…

Despite our present-day inability to predict the topology of the universe it is expected that we should be able to detect it in the near future. A nontrivial detectable topology of the space section of the universe can be probed for all…

In this paper, we consider the scattering of a time-dependent electromagnetic wave by an elastic body immersed in the lower half-space of a two-layered background medium which is separated by an unbounded rough surface. By proposing two…

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…

We prove a general lower bound on Christoffel function on planar convex domains in terms of a modification of the parallel section function of the domain. For a certain class of planar convex domains, in combination with a recent general…

In the recent letter Pearce et. al. Phys. Rev. Lett. 122, 168002 (2019) the authors investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal which is constrained to the surface of a torus. The underlying model…

We solve the $\partial \bar{\partial}$-problem for the differential forms of class $C^\infty$ with boundary value in currents sense defined on a contractible completely strictly pseudoconvex domain of a complex manifold.

The dynamics of a gravitational torsion kink as a plane symmetric thick domain wall solution of Einstein-Cartan (EC) field equation is given. The spin-torsion energy has to be as high as the gravitational kink potential otherwise torsion…

Motivated by the study of the corner singularities in the so-called cavity flow, we establish in this article, the existence and uniqueness of solutions in $L^2(\Omega)^2$ for the Stokes problem in a domain $\Omega,$ when $\Omega$ is a…