Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A class of comparison theorems for nonselfadjoint elliptic equations.


Author: Kurt Kreith
Journal: Proc. Amer. Math. Soc. 29 (1971), 547-552
MSC: Primary 35.11
DOI: https://doi.org/10.1090/S0002-9939-1971-0279418-8
MathSciNet review: 0279418
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Seemingly disparate comparison theorems for nonselfadjoint elliptic equations have been established by C. A. Swanson and the author. The present paper establishes a class of comparison theorems involving an arbitrary vector valued function $ p(x)$. Special choices of $ p(x)$ yield both of the comparison theorems cited above.


References [Enhancements On Off] (What's this?)

  • [1] M. H. Protter, A comparison theorem for elliptic equations, Proc. Amer. Math. Soc. 10 (1959), 296-299. MR 21 #5803. MR 0107076 (21:5803)
  • [2] C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611-616. MR 34 #1663. MR 0201781 (34:1663)
  • [3] K. Kreith, A comparison theorem for general elliptic equations with mixed boundary conditions, J. Differential Equations 8 (1970), 537-541. MR 0265737 (42:646)
  • [4] E. Picard, Leçons sur quelques problèmes aux limites de la théorie des équations différentielles, Paris, 1930.
  • [5] M. Picone, Un teorema sulle soluzioni delle equazioni lineari ellitiche autoaggiunte alle derivate parziali del secondo ordine, Atti. Accad. Lincei 20 (1911), 341-344.
  • [6] K. Kreith, A remark on a comparison theorem of Swanson, Proc. Amer. Math. Soc. 20 (1969), 549-550. MR 38 #4798. MR 0236503 (38:4798)
  • [7] C. A. Swanson, Comparison theorems for elliptic equations on unbounded domains, Trans. Amer. Math. Soc. 126 (1967), 278-285. MR 34 #3064. MR 0203211 (34:3064)
  • [8] -, An identity for elliptic equations with applications, Trans. Amer. Math. Soc. 134 (1968), 325-333. MR 38 #400. MR 0232074 (38:400)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35.11

Retrieve articles in all journals with MSC: 35.11


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0279418-8
Keywords: Nonselfadjoint elliptic equations, Picone identity, mixed boundary condition, Green's theorem
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society