This article is cited in 12 scientific papers (total in 12 papers)
Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application
N. V. Kislov
Let $A$ and $B$ be symmetric operators in a Hilbert space $H$, such that $B$ is positive and $A$ has an arbitrary spectrum. In this paper nonhomogeneous boundary value problems are considered for an equation of the form
An abstract theorem (of the Lax–Milgram type) is proved, which is then used to prove theorems on the weak and strong solvability of boundary value problems for equation (1) in the energy spaces defined by the operators $A$ and $B$, as well as a theorem on the traces of a strong solution.
As an application, nonhomogeneous boundary value problems for partial differential equations are considered.
Bibliography: 16 titles.
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Mathematics of the USSR-Sbornik, 1986, 53:1, 17–35
MSC: Primary 35M05, 47A50, 47F05; Secondary 35R20
N. V. Kislov, “Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application”, Mat. Sb. (N.S.), 125(167):1(9) (1984), 19–37; Math. USSR-Sb., 53:1 (1986), 17–35
Citation in format AMSBIB
\paper Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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