Related papers: A sharp Korn's inequality for piecewise $H^1$ spac…

In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball…

The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions…

In this short article we obtain some necessary conditions for a so-called fractional Hardy-Sobolev's inequalities in multidimensional case. We also give some examples to show the sharpness of these inequalities.

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

Collisional breakage in the particulate process has a lot of recent curiosity. We study the pure collisional breakage equation which is nonlinear in nature accompanied by locally bounded breakage kernel and collision kernel. The continuous…

This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when the position of an isolated discontinuity in the function and…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

In this manuscript two $BMO$ estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the $BMO$-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the…

We prove a Heinz type inequality for harmonic diffeomorphisms of of the half-plane onto itself. We then apply this result to prove some sharp bound of the Gaussian curvature of a minimal surface, provided that it lies above the whole…

This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…

In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

We study inequalities connecting the product of uniform norms of polynomials with the norm of their product. This circle of problems include the Gelfond-Mahler inequality for the unit disk and the Kneser-Borwein inequality for the segment…

We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical…

We obtain sharp estimate on $p$-spectral gaps, or equivalently optimal constant in $p$-Poincar\'e inequalities, for metric measure spaces satisfying measure contraction property. We also prove the rigidity for the sharp $p$-spectral gap.

A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shells for zero or periodic Dirichlet, Neumann, and Robin type…

We investigate the character of the linear constraints which are needed for Poincar\'e and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a…