Green’s Formulas for Cone Differential Operators

نویسنده

  • INGO WITT
چکیده

Green’s formulas for elliptic cone differential operators are established. This is done by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint, thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green’s formulas are deduced. CONTENTS

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

We consider solution operators of linear ordinary boundary problems with “too many” boundary conditions, which are not always solvable. These generalized Green’s operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green’s operators is again a generalized Green’s operator for the product of the corresponding d...

متن کامل

Regular and Singular Boundary Problems in Maple

We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and Green’s operators, we employ the algebra of integro-differential operators. The operations implemented for regular boundary problems include computing Green’s ...

متن کامل

Estimates on Green functions of second order differential operators with singular coefficients

We investigate the Green’s functions G(x;x′) of some second order differential operators on R with singular coefficients depending only on one coordinate x0. We express the Green’s functions by means of the Brownian motion. Applying probabilistic methods we prove that when x = (0,x) and x′ = (0, x′) (here x0 = 0) lie on the singular hyperplanes then G(0,x; 0, x′) is more regular than the Green’...

متن کامل

Solving and factoring boundary problems for linear ordinary differential equations in differential algebras

We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integro-differential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions...

متن کامل

Methods of Extending Lower Order Problems to Higher Order Problems in the Context of Smallest Eigenvalue Comparisons

The theory of u0-positive operators with respect to a cone in a Banach space is applied to the linear differential equations u + λ1p(x)u = 0 and u + λ2q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions u(0) = u(r) = u(r) = u(1) = 0, 0 < r < 1. The existence of smallest positive eigenvalues is established, and a comparison theorem for smallest positive eigenvalues is obtained. Th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003