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Mat. Sb., 1998, Volume 189, Number 1, Pages 45–78 (Mi msb292)  

This article is cited in 13 scientific papers (total in 13 papers)

On non-negative contractive semigroups with non-local conditions

E. I. Galakhov, A. L. Skubachevskii

Moscow Aviation Institute

Abstract: A second-order elliptic operator with non-local conditions in a bounded domain $Q\subset \mathbb R^n$ with boundary $\partial Q\in C^\infty$ is considered. The so-called 'non-transversal' case is investigated, that is, the case when the value of a function at each point $x\in \partial Q$ is related to the integral of this function over $\overline Q$ with respect to some Borel measure $\mu (x,dy)$. Sufficient conditions for the existence of a Feller semigroup whose infinitesimal generator is the closure in $C(\overline Q)$ of the elliptic operator under consideration are obtained.


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English version:
Sbornik: Mathematics, 1998, 189:1, 43–74

Bibliographic databases:

UDC: 519.21+517.95
MSC: 47F05, 47D03
Received: 11.02.1997

Citation: E. I. Galakhov, A. L. Skubachevskii, “On non-negative contractive semigroups with non-local conditions”, Mat. Sb., 189:1 (1998), 45–78; Sb. Math., 189:1 (1998), 43–74

Citation in format AMSBIB
\by E.~I.~Galakhov, A.~L.~Skubachevskii
\paper On non-negative contractive semigroups with non-local conditions
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 1
\pages 45--78
\jour Sb. Math.
\yr 1998
\vol 189
\issue 1
\pages 43--74

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    This publication is cited in the following articles:
    1. A. K. Gushchin, “Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation”, Sb. Math., 189:7 (1998), 1009–1045  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Gushchin, AK, “A condition for complete continuity of the operators arising in nonlocal problems for elliptic equations”, Doklady Mathematics, 62:1 (2000), 32  mathscinet  zmath  isi  elib
    3. Galakhov, EI, “On Feller semigroups generated by elliptic operators with integro-differential boundary conditions”, Journal of Differential Equations, 176:2 (2001), 315  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    4. A. K. Gushchin, “A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations”, Sb. Math., 193:5 (2002), 649–668  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. L. Skubachevskii, “Nonclassical boundary value problems. I”, Journal of Mathematical Sciences, 155:2 (2008), 199–334  mathnet  crossref  mathscinet  zmath  elib
    6. P. L. Gurevich, “Bounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Conditions near the Boundary”, Math. Notes, 83:2 (2008), 162–179  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. P. L. Gurevich, “On the Existence of a Feller Semigroup with Atomic Measure in a Nonlocal Boundary Condition”, Proc. Steklov Inst. Math., 260 (2008), 157–171  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. A. L. Skubachevskii, “On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems”, Proc. Steklov Inst. Math., 260 (2008), 238–253  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. A. L. Skubachevskii, “Nonclassical boundary-value problems. II”, Journal of Mathematical Sciences, 166:4 (2010), 377–561  mathnet  crossref  mathscinet  elib
    10. Ratyni A.K., “On the solvability of the first nonlocal boundary value problem for an elliptic equation”, Differ. Equ., 45:6 (2009), 862–872  crossref  mathscinet  zmath  isi  elib  elib  scopus
    11. P. L. Gurevich, “Elliptic problems with nonlocal boundary conditions and Feller semigroups”, Journal of Mathematical Sciences, 182:3 (2012), 255–440  mathnet  crossref  mathscinet  zmath
    12. A. A. Petrova, V. V. Smagin, “Convergence of the Galyorkin method of approximate solving of parabolic equation with weight integral condition on a solution”, Russian Math. (Iz. VUZ), 60:8 (2016), 42–51  mathnet  crossref  isi
    13. L. E. Rossovskii, A. R. Khanalyev, “Koertsitivnaya razreshimost nelokalnykh kraevykh zadach dlya parabolicheskikh uravnenii”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 140–151  mathnet
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