Upper and lower bounds for quadratic functionals $(*)$

• Díaz, Joaquin B. ^[1]
  1. [1] University of Maryland, College Park

     University of Maryland, College Park

     Estados Unidos

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 4, Fasc. 2, 1951, págs. 3-50
• Idioma: inglés
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• Resumen

  • The paper gives a systematic procedure for obtaining monotone sequences of upper and lover bounds for quadratic integrals such as those encountered in torsional rigidity, capacity, and other physical quantities. The monotone sequences are obtained from Bessel's inequality, while maximum and minimum principles for the solutions of the boundary value problems are obtained from Schwarz' inequality.