5
Views
0
CrossRef citations to date
0
Altmetric
Review Article

On the generalized Farwig problem for a polyharmonic equation

ORCID Icon
Received 25 Aug 2023, Accepted 24 Jun 2024, Published online: 03 Jul 2024

References

  • Soboleff S. Sur un problème limite pour les équations polyharmoniques. Rec Math [Mat Sbornik] NS. 1937;2(3):465–499.
  • Sobolev SL. Some applications of functional analysis in mathematical physics. 3rd ed. Moscow: Nauka; 1988. Applications of Functional Analysis in Mathematical Physics. Providence (RI): American Mathematical Society; 1991.
  • Farwig R. A note on the reflection principle for the biharmonic equation and the Stokes system. Acta Appl Math. 1994;37:41–51. doi: 10.1007/BF00995128
  • Agmon S, Douglis A, Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Commun Pure Appl Math. 1959;12:623–727. doi: 10.1002/cpa.v12:4
  • Gazzola F, Grunau H-C, Sweers G. Polyharmonic boundary value problems. Berlin: Springer; 2010. (Lecture Notes in Mathematics; Vol. 1991).
  • Friedrichs KO. Die Randwert- und Eigenwert-Probleme aus der Theorie des elastischen Platten. Math Annalen. 1928;98:205–247. http://eudml.org/doc/159211.
  • Akel M, Begehr H, Mohammed A. Integral representations in the complex plane and iterated boundary value problems. Rocky Mt J Math. 2022;52(2):381–413. doi: 10.1216/rmj.2022.52.381
  • Begehr H, Vu TNH, Zhang Z-X. Polyharmonic Dirichlet problems. Proc Steklov Math Inst. 2006;255:13–34. doi: 10.1134/S0081543806040031
  • Begehr H, Vanegas CJ. Iterated Neumann problem for the higher order Poisson equation. Math Nachr. 2006;279:38–57. doi: 10.1002/mana.v279:1/2
  • Begehr H, Gaertner E. A Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane. Georgian Math J. 2007;14(1):33–52. doi: 10.1515/GMJ.2007.33
  • Begehr H, Du J, Wang Y. A Dirichlet problem for polyharmonic functions. Ann Mat Pura Appl. 2008;187(3):435–457. doi: 10.1007/s10231-007-0050-5
  • Egorov YV, Kondratiev VA. On spectral theory of elliptic operators. Basel: Birkhauser; 1996.
  • Kondrat'ev VA, Oleinik OA. Boundary value problems for the system of elasticity theory in unbounded domains. Korn's inequalities. Russ Math Surv. 1988;43(5):65–119. doi: 10.1070/RM1988v043n05ABEH001945
  • Kondratiev VA, Oleinik OA. Hardy's and Korn's inequality and their application. Rend Mat Appl. 1990;10(3):641–666. Serie VII.
  • Matevossian OA. Solutions of exterior boundary value problems for the elasticity system in weighted spaces. Sbornik Math. 2001;192(12):1763–1798. doi: 10.1070/SM2001v192n12ABEH000615
  • Matevossian HA. On solutions of mixed boundary-value problems for the elasticity system in unbounded domains. Izvestiya Math. 2003;67(5):895–929. doi: 10.1070/IM2003v067n05ABEH000451
  • Matevossian HA. On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains. P-Adic Numbers Ultrametric Anal Appl. 2015;7(1):71–75. doi: 10.1134/S2070046615010069
  • Matevosyan OA. On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains. Russ J Math Phys. 2016;23(1):135–138. doi: 10.1134/S106192081601012X
  • Matevosyan OA. On solutions of one boundary value problem for the biharmonic equation. Differ Equ. 2016;52(10):1379–1383. doi: 10.1134/S0012266116100153
  • Matevossian HA. On the biharmonic Steklov problem in weighted spaces. Russ J Math Phys. 2017;24(1):134–138. doi: 10.1134/S1061920817010125
  • Matevossian HA. On the Steklov-type biharmonic problem in unbounded domains. Russ J Math Phys. 2018;25(2):271–276. doi: 10.1134/S1061920818020115
  • Matevossian HA. On the polyharmonic Neumann problem in weighted spaces. Complex Var Elliptic Equ. 2019;64(1):1–7. doi: 10.1080/17476933.2017.1409740
  • Matevossian HA. Asymptotics and uniqueness of solutions of the elasticity system with the mixed Dirichlet–Robin boundary conditions. MDPI Math. 2020;8(12):2241. 32 pp.
  • Migliaccio G, Matevossian HA. Exterior biharmonic problem with the mixed Steklov and Steklov-type boundary conditions. Lobachevskii J Math. 2021;42(8):1886–1899. doi: 10.1134/S1995080221080205
  • Migliaccio G, Matevossian HA. Steklov–Farwig biharmonic problem in exterior domains. Lobachevskii J Math. 2023;44(6):2413–2428. doi: 10.1134/S1995080223060379
  • Kondratiev VA, Oleinik OA. On the behavior at infinity of solutions of elliptic systems with a finite energy integral. Arch Rat Mech Anal. 1987;99(1):75–89. doi: 10.1007/BF00251392
  • Douglis A, Nirenberg L. Interior estimates for elliptic systems of partial differential equations. Commun Pure Appl Math. 1955;8:503–538. doi: 10.1002/cpa.v8:4
  • Morrey CB. Multiple integrals in the calculus variations. Berlin: Springer; 1966.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.