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General boundary value problems for elliptic partial differential equations
Author(s) -
Schechter Martin
Publication year - 1959
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160120305
Subject(s) - mathematics , boundary value problem , mathematical economics , pure mathematics , mathematical analysis
does not vanish in R for real £?^0. If R is the closure G of a bounded domain G, we shall say that A is properly elliptic in G if in addition it satisfies at every point x on the boundary G of G (cf. [2; S; 8]). CONDITION 1. For every real vector TT^O parallel to G at x and every real VT^O normal to G at x, the polynomial P{z) = P(x, r-\-zv) has exactly r roots Xfc(r, J>), & = 1, 2, • • • , r, with positive imaginary parts. If n>2, all elliptic operators are properly elliptic. By a boundary operator we shall mean a linear partial differential operator whose coefficients need merely be defined on G. If