Notes on Generalized Boundary Value Problems in Banach Spaces. I. Adjoint and Extension Theory.

Abstract

Multipoint boundary conditions arise in the theory of beams or plates with interior point loads, and also the mathematical theory of splines. Interface conditions arise in problems of diffusion through parallel 'slabs' with different properties (e.g., nuclear reactors or the study of shock waves). Adjoints of such differential operators also are encountered when one attempts to derive Euler-Lagrange equations for constrained minimization problems. Our method is very general and is designed to work for partial differential, integral and functional differential operators as well as differential operators. Part I presents some of the abstract machinery to solve the problem. Part II will apply this machinery to concrete and applied problems of the type mentioned above.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1980
Accession Number
ADA086371

Entities

People

  • R. C. Brown

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Calculus
  • Calculus Of Variations
  • Computations
  • Construction
  • Equations
  • Hilbert Space
  • Hypotheses
  • Integral Equations
  • Mathematics
  • Notation
  • Topology
  • United States
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

Technology Areas

  • Space