RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb. (N.S.), 1970, Volume 83(125), Number 2(10), Pages 181–213 (Mi msb3507)

Homeomorphism theorems and a Green's formula for general elliptic boundary problems with nonnormal boundary conditions

Ya. A. Roitberg

Abstract: 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, 5Â268; 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.

Full text: PDF file (3014 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1970, 12:2, 177–212

Bibliographic databases:

UDC: 517.946
MSC: 58D05, 26B20, 35J55, 35S15, 35S05

Citation: 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

Citation in format AMSBIB
\Bibitem{Roi70} \by Ya.~A.~Roitberg \paper Homeomorphism theorems and a~Green's formula for general elliptic boundary problems with nonnormal boundary conditions \jour Mat. Sb. (N.S.) \yr 1970 \vol 83(125) \issue 2(10) \pages 181--213 \mathnet{http://mi.mathnet.ru/msb3507} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=300155} \zmath{https://zbmath.org/?q=an:0216.12503} \transl \jour Math. USSR-Sb. \yr 1970 \vol 12 \issue 2 \pages 177--212 \crossref{https://doi.org/10.1070/SM1970v012n02ABEH000916} 

• http://mi.mathnet.ru/eng/msb3507
• http://mi.mathnet.ru/eng/msb/v125/i2/p181

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Ya. A. Roitberg, “On boundary values of generalized solutions of elliptic equations”, Math. USSR-Sb., 15:2 (1971), 241–260
2. 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
•  Number of views: This page: 284 Full text: 99 References: 43