Related papers: An overview on the Cheeger problem
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…
Initial value problems for the integrable discrete equations on quad-graphs are investigated. A geometric criterion of the well-posedness of such a problem is found. The effects of the interaction of the solutions with the localized defects…
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and…
The Riemann curvature tensor is a central mathematical tool in Einstein's theory of general relativity. Its related eigenproblem plays an important role in mathematics and physics. We extend M-eigenvalues for the elasticity tensor to the…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes…
An example of a solution branch of the three dimensional Euler equation Cauchy problem is constructed which develops a singular velocity component and a singular vorticity component after finite time for some data which have Hoelder…
A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
Expository article on the problem of determining the maximum number of equiangular lines with a fixed angle, and the associated problem of second eigenvalue multiplicity in graphs.
In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy estimates on derivatives. As an application, we use Donnelly…
In this paper, we study a Schr\"odinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation in the case of partial wetting. We also obtain the Schauder estimates…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.