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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 6, Pages 71–110 (Mi izv460)  

This article is cited in 6 scientific papers (total in 6 papers)

Non-local elliptic problems with non-linear argument transformations near the points of conjugation

P. L. Gurevich


Abstract: We consider elliptic equations of order $2m$ in a domain $G\subset\mathbb R^n$ with non-local conditions that connect the values of the unknown function and its derivatives on $(n-1)$-dimensional submanifolds $\overline\Upsilon_i$ (where $\bigcup_i\overline\Upsilon_i=\partial G$ with the values on $\omega_{is}(\overline\Upsilon_i)\subset\overline G$. Non-local elliptic problems in dihedral angles arise as model problems near the conjugation points $g\in\overline\Upsilon_i\cap \overline\Upsilon_j\ne\varnothing$, $i\ne j$. We study the case when the transformations $\omega_{is}$ correspond to non-linear transformations in the model problems. It is proved that the operator of the problem remains Fredholm and its index does not change as we pass from linear argument transformations to non-linear ones.

DOI: https://doi.org/10.4213/im460

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English version:
Izvestiya: Mathematics, 2003, 67:6, 1149–1186

Bibliographic databases:

UDC: 517.9
MSC: 35J40, 46E35, 47F05, 47A53
Received: 15.03.2002

Citation: P. L. Gurevich, “Non-local elliptic problems with non-linear argument transformations near the points of conjugation”, Izv. RAN. Ser. Mat., 67:6 (2003), 71–110; Izv. Math., 67:6 (2003), 1149–1186

Citation in format AMSBIB
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    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. Soldatov A. P., “The Bitsadze-Samarskii problem for Douglis analytic functions”, Differ. Equ., 41:3 (2005), 416–428  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. L. Gurevich, “Generalized Solutions of Nonlocal Elliptic Problems”, Math. Notes, 77:5 (2005), 614–629  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Soldatov A.P., “Problem of Bitsadze-Samarskii type for second-order elliptic systems in the plane”, Dokl. Math., 74:2 (2006), 736–740  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. A. L. Skubachevskii, “Nonclassical boundary value problems. I”, Journal of Mathematical Sciences, 155:2 (2008), 199–334  mathnet  crossref  mathscinet  zmath  elib
    5. A. L. Skubachevskii, “Nonclassical boundary-value problems. II”, Journal of Mathematical Sciences, 166:4 (2010), 377–561  mathnet  crossref  mathscinet  elib
    6. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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