Functional Analysis Approach for the Derivation of Hybrid Variational Functionals.

Abstract

The original boundary value problems is embedded in a larger class of b.v. problem pertaining to physical quantities of tensorial order higher than that of the original problem. The new b.v. problem is interpreted as defining an isomorphism between two appropriate Hilbert spaces; the constraint space and the solution space H, the unique solution of the original b.v. problem being thus characterized as the unique element of H satisfying a prescribed set of constraints. Then variational formulations are deduced by: (1) defining subsets of H satisfying an arbitrary number of such constraints (thus generalizing the notions of 'equilibrating' and 'compatible' solutions); (2) characterizing the solution vector as the unique element common to two such subsets; (3) finding the appropriate functional, defined over these two subsets, which is rendered stationary (in particular minimum) by the exact solution.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1975
Accession Number
ADA023432

Entities

People

  • L. G. Napolitano

Organizations

  • University of Naples Federico II

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Functional Analysis
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space