Abstract:
One gives a survey and one presents the method of the reduction of a general boundary-value problem to a Dirichlet type problem, based on the systematic use of the concept of a weighted pseudodifferential operator. One gives the fundamental results in the theory of weighted spaces of functions. The survey is compiled on the basis of the publications refereed during 1970–1983 in the Referativnyi Zhurnal “Matematika” and on the basis of the latest results published in the form of reports or preprints or deposited at VINITI.
Citation:
V. P. Glushko, Yu. B. Savchenko, “Higher-order degenerate elliptic equations: spaces, operators and boundary value problems”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 23, VINITI, Moscow, 1985, 125–218; J. Soviet Math., 39:6 (1987), 3088–3148
A. V. Glushko, A. D. Baev, D. S. Shumeeva, “Asimptotika v okrestnosti tochki vyrozhdeniya resheniya uravneniya teploprovodnosti s silnym vyrozhdeniem”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 11:1 (2011), 9–19
M. S. Bichegkuev, “Vzveshennaya proizvodnaya i differentsialnye uravneniya”, Vladikavk. matem. zhurn., 5:4 (2003), 32–42
M. S. Bichegkuev, “Integralnye operatory vzveshennoi svertki”, Vladikavk. matem. zhurn., 4:2 (2002), 17–22
Vladimir Rabinovich, Bert-Wolfgang Schulze, Nikolai Tarkhanov, “A Calculus of Boundary Value Problems in Domains with Non-Lipschitz Singula Points”, Math. Nachr., 215:1 (2000), 115
M. S. Bichegkuev, “Vzveshennaya proizvodnaya i differentsialnye uravneniya”, Vladikavk. matem. zhurn., 1:3 (1999), 5–17
V. P. Glushko, N. A. Yartseva, “An elliptic periodic problem with degeneracy in Lp”, Math. Notes, 63:4 (1998), 552–556
M. S. Bichegkuev, “Integral operators generated by weighted shift operators”, Math. Notes, 59:3 (1996), 321–323
V. P. Glushko, S. A. Tkacheva, “Heat equation with degeneration in Holder and Slobodetskii spaces”, Math. Notes, 58:2 (1995), 803–813
S. Z. Levendorskii, “On types of degenerate elliptic operators”, Math. USSR-Sb., 66:2 (1990), 523–540
Citation in format AMSBIB
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