On inequalities for differential operators

On Inequalities for Differential Operators

In this paper we study the following problem: Given that certain functionals of u and its derivatives belong to given Lclasses over the infinite interval, what can be said about the L-classes of other functionals? Utilizing a simple device from the theory of linear differential equations, we obtain a number of results due to Landau, Kolmogoroff, Halperin-von Neumann, and Nagy, together with som...

Weighted Inequalities for Potential Operators on Differential Forms

Lieb-thirring Inequalities for Higher Order Differential Operators

We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order γ≥3/4 for a fourth order operator in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators, in dimensions greater than one. For the critical case γ=1−1/(2l) in dimension d=1 with l≥2 we prove the inequality L0l,γ,d < Ll,γ,d , which holds in contrast to cu...

Submajorization inequalities associated with $tau$-measurable operators

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...