This article is cited in 2 scientific papers (total in 2 papers)
Homeomorphism theorems and a Green's formula for general elliptic boundary problems with nonnormal boundary conditions
Ya. A. Roitberg
Theorems on homeomorphisms for elliptic operators have been established by several mathematicians (Lions, Magenes, Schechter, Yu. M. Berezanskii, S. G. Krein, Ya. A. Roitberg and others; see RZhMat., 1962, 5B321; 1963, 5В268; 1964, 3B341, 12B286; 1965, 4B255; 1966, 3B321; 1968, 4B368, 11B309; 1969, 2B314.k). In their work it was always assumed that the boundary conditions are normal in the sense of Aronszajn–Milgram–Schechter. But in the present article the theorems on homeomorphisms are established without the assumption that the boundary expressions are normal; they may be pseudodifferential in the directions tangent to the boundary and differential in the normal directions. Essential use is made of the Green's formula developed for the case of the boundary conditions here in question. A study is also made of a problem formally adjoint to an elliptic problem with respect to Green's formula and the homeomorphism theorem is established for this problem as well.
Bibliography: 36 titles.
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Mathematics of the USSR-Sbornik, 1970, 12:2, 177–212
MSC: 58D05, 26B20, 35J55, 35S15, 35S05
Ya. A. Roitberg, “Homeomorphism theorems and a Green's formula for general elliptic boundary problems with nonnormal boundary conditions”, Mat. Sb. (N.S.), 83(125):2(10) (1970), 181–213; Math. USSR-Sb., 12:2 (1970), 177–212
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\paper Homeomorphism theorems and a~Green's formula for general elliptic boundary problems with nonnormal boundary conditions
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
Ya. A. Roitberg, “On boundary values of generalized solutions of elliptic equations”, Math. USSR-Sb., 15:2 (1971), 241–260
A. S. Dikanskii, “Conjugate problems of elliptic differential and pseudodifferential boundary value problems in a bounded domain”, Math. USSR-Sb., 20:1 (1973), 67–83
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