Related papers: A note on Perelman's LYH inequality

We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

In this paper we establish improved Hardy and Rellich type inequalities on Riemannian manifold $M$. Furthermore, we also obtain sharp constant for the improved Hardy inequality and explicit constant for the Rellich inequality on hyperbolic…

We obtain a Lundberg-type inequality in the case of an inhomogeneous renewal risk model. We consider the model with independent, but not necessarily identically distributed, claim sizes and the interoccurrence times. In order to prove the…

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.

We obtain an improvement of the John-Nirenberg inequality for the series of the form $\sum_{n=1}^{\infty}n^{-1}e^{2\pi i n^k x},\;k>2,$ on intervals consisting of points of a same convergent of their continued fractions. We also establish a…

We describe the close connection between the linear system for the sixth Painlev\'e equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions and show how, in the case of reducible monodromy, the…

We consider the Brascamp--Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of…

We give a sufficient condition for existence of an exponential dichotomy for a general linear dynamical system (not necessarily invertible) in a Banach space, in discrete or continuous time. We provide applications to the backward heat…

The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without…

We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of majorants and the properties of the Newton polygon, we…

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form $A(u) + |u|^{q-1}u \leq A(v) + |v|^{q-1}v$ on ${\Bbb R}^n$, where $n\geq 1$, $q$ is…

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…

We study the existence and regularity of solutions to the Cauchy problem for the inhomogeneous heat equation on compact Riemannian manifolds with conical singularities. We introduce weighted H\"older and Sobolev spaces with discrete…

This paper extends the nonabelian Hodge correspondence for Kaehler manifolds to a larger class of hermitian metrics on complex manifolds called balanced of Hodge-Riemann type. Essentially, it grows out of a few key observations so that the…

There was proposed the method of a factorization of PDE. The method is based on reduction of complicated systems to more easy ones (for example, due to dimension decrease). This concept is proposed in general case for the arbitrary PDE…

In this paper, we prove Hamilton's Harnack inequality and the gradient estimates of the logarithmic heat kernel for the Witten Laplacian on complete Riemainnian manifolds. As applications, we prove the $W$-entropy formula for the Witten…

We prove an inequality of H\"older type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness…

In this survey we give a compact presentation of well-known functional inequalities of Hardy and Rellich type in the $L^2$ setting. In addition, we give some insights of their proofs by using standard and basic tools such as the method of…