Related papers: Two inequalities for convex equipotential surfaces
Both analytic and geometric forms of an optimal monotone principle for $L^p$-integral of the Green function of a simply-connected planar domain $\Omega$ with rectifiable simple curve as boundary are established through a sharp…
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
We establish pointwise estimates for the Green function to the Dirichlet problem for parabolic equation with coefficients measurable in time variable. Using these estimate we obtain coercive estimates for this problem in anisotropic…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…
Lie symmetries of a Novikov geometrically integrable equation are found and group-invariant solutions are obtained. Local conservation laws up to second order are established as well as their corresponding conserved quantities. Sufficient…
In this note we study the Dirichlet problem associated with a version of prime end boundary of a bounded domain in a complete metric measure space equipped with a doubling measure supporting a Poincare inequality. We show the resolutivity…
In this paper, we investigate boundary estimates for the Dirichlet problem for a class of fully nonlinear elliptic equations with general boundary conditions, including nonzero boundary conditions. Given specific structural conditions on…
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…
Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argument, we derive a general existence result for surfaces with…
In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on…
In the paper we study the 2D div-curl problem in the exterior domain which models the flow with given vorticity, divergency, boundary condition at infinity, and Dirichlet condition on the solid surface. We will find the relations on…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…
For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…