Direct and inverse estimates for Phillips type operators

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...

Upper Estimates in Direct Inequalities for Bernstein-Type Operators

We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as Weierstrass, Sza sz, and Bernstein opera...

Inverse Estimates for Lupas-Baskakov Operators

We establish Stechkin-Marchaud-type inequalities for some Feller operators by using some modified Ditzian-Totik modulus of smooth -ness. Then we derive some inverse results for this family of operators. Moreover combining the inverse results with the direct estimates we obtain a approximation equivalent theorem.

Novel Inverse Estimates for Non-Local Operators

Carleman Estimates and Inverse Problems for Dirac Operators

We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that harmonic functions can be considered as limiting Carleman weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator.