A Boundary Value Problem for Higher Order Elliptic Equations in Many Connected Domain on the Plane

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2017.3.7130 A Boundary Value Problem for Higher Order Elliptic Equations in Many Connected Domain on the Plane Soldatov A. P. Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 3. Abstract: For the elliptic equation of \(2l\)th order with constant (and leading) coefficients boundary value a problem with normal derivatives of the \((k_j-1)-\)order, \(j=1,\ldots,l\) considered. Here \(1\le k_1 <\ldots< k_l\le 2l\). When \(k_j=j\) it moves to the Dirichlet problem, and when \)k_j = j + 1\) it corresponds to the Neumann problem. The sufficient condition of the Fredholm problem and index formula are given. Keywords: elliptic equation, boundary value problem, normal derivatives, many connected domain, smooth contour, Fredholm property, index formula Language: Russian Download the full text For citation: Soldatov A. P. A boundary value problem for higher order elliptic equations in many connected domain on the plane Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 51-58. DOI 10.23671/VNC.2017.3.7130 + References 1. Bitsadze A.V. To Neumann problem for harmonic functions. Dokl. AN SSSR, 1990, vol. 311, no. 1. 2. Malahova N.A., Soldatov A.P. On boundary value problem for a elliptic equation of high order. Differentsial’nye Uravneniya [Differential Equations], 2008, vol. 44, no. 8, pp. 1077-1083 (in Russian). 3. Koshanov B. D., Soldatov A. P. Boundary Value Problem with Normal Derivatives for a Higher-Order Elliptic Equation on the Plane. Differentsial’nye Uravneniya [Differential Equations], 2016, vol. 52, no. 12, pp. 1666–1681 (in Russian). 4. Vaschenko O. V., Soldatov A. P. Integral representation of solutions of the generalized Beltramy system, Nauchnie vedomosti BelGU, 2006, vol. 6, no. 1(21), pp. 3-6 (in Russian). 5. Soldatov A. P. Singular integral operators and elliptic boundary value problems. Sovremen. matematika. Fundament. napravleniya [Contemporary Mathematics. Fundamental Directions], 2016, vol. 63, pp. 1-179 (in Russian). 6. Soldatov A. P. Hyperanalytic functions and their applications, J. Math. Sciences, 2004, vol. 17, P. 1-111. 7. Abapolova E. A., Soldatov A. P. To the theory of singular integral equations on a smooth contour, Nauchnie vedomosti BelGU [Belgorod State University Scientific Bulletin], 2010, no. 5(76), issue 18, pp. 6-20. 8. Mushelishvili N. I. Singular Integral Equations. Noordhoff, Groningen, 1953. 9. Soldatov A. P. A function theory method in boundary value problems in the plane. I. A smooth case. Izvestiya AN USSR. Ser. Matem., 1992, vol. 39, no. 2, pp. 1070-1100 (in Russian). 10. Soldatov A.P. The Schvarts problem for Douglis analytic functions, Sovremennaya Matematika i ee Prilozheniya, 2010, vol. 67, pp. 99-102 (in Russian). 11. Palais P. Seminar on the Atiya-Singer Theorem. Princeton, Univers. Press Princeton, 1965. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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