ON THE CAUCHY PROBLEM OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Lecture Notes on Elliptic Partial Differential Equations

An Eigenvalue Problem for Nonlinear Elliptic Partial Differential Equations

where X is a real number and/(i,x) is a real-valued function defined on R1 x G with /(0, x) s 0. If/(u,x) = u, the study of the boundary value problem (1) forms the foundation of the spectral analysis of A, a problem of great importance both in mathematics and its applications. If f(u,x) does not depend on « in a linear manner, one enters the relatively uncharted world of nonlinear functional a...

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...

The Stability for the Cauchy Problem for Elliptic Equations *

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, th...

On the Construction of Discretizations of Elliptic Partial Differential Equations

Dedicated to Gerry Ladas on the occasion of his 60th Birthday Algorithmic aspects of a class of nite element collocation methods for the approximate numerical solution of elliptic partial diierential equations are described. Locally, for each nite element, the approximate solution is a polynomial. Polynomials corresponding to adjacent nite elements need not match continuously, but their values ...