A class of comparison theorems for nonselfadjoint elliptic equations.

Kreith, Kurt

doi:10.1090/S0002-9939-1971-0279418-8

A class of comparison theorems for nonselfadjoint elliptic equations.
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Proc. Amer. Math. Soc. 29 (1971), 547-552 Request permission

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

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C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611–616. MR 201781, DOI 10.1090/S0002-9939-1966-0201781-2
Kurt Kreith, A comparison theorem for general elliptic equations with mixed boundary conditions, J. Differential Equations 8 (1970), 537–541. MR 265737, DOI 10.1016/0022-0396(70)90026-4

Leçons sur quelques problèmes aux limites de la théorie des équations différentielles

Un teorema sulle soluzioni delle equazioni lineari ellitiche autoaggiunte alle derivate parziali del secondo ordine

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Kurt Kreith, A remark on a comparison theorem of Swanson, Proc. Amer. Math. Soc. 20 (1969), 549–550. MR 236503, DOI 10.1090/S0002-9939-1969-0236503-5
C. A. Swanson, Comparison theorems for elliptic equations on unbounded domains, Trans. Amer. Math. Soc. 126 (1967), 278–285. MR 203211, DOI 10.1090/S0002-9947-1967-0203211-9
C. A. Swanson, An identity for elliptic equations with applications, Trans. Amer. Math. Soc. 134 (1968), 325–333. MR 232074, DOI 10.1090/S0002-9947-1968-0232074-1