On the polyharmonic Neumann problem in weighted spaces

References

• Gazzola F , Grunau HCh , Sweers G . Polyharmonic boundary value problems. Vol. 1991, Lecture Notes in Mathematics. Berlin: Springer-Verlag; 2010.
   Google Scholar
• Farwig R . A note on the reflection principle for the biharmonic equation and the Stokes system. Acta Appl Math. 1994;34:41–51.
   Google Scholar
• Begehr H . Dirichlet problems for the biharmonic equation. General Math. 2005;13:65–72.
   Google Scholar
• Begehr H , Vu TNH , Zhang Z-X . Polyharmonic Dirchlet problems. Proc Steklov Math Inst. 2006;255:13–34.
   Google Scholar
• Begehr H , Vagenas CJ . Iterated Neumann problem for the higher order Poisson equation. Math Nachr. 2006;279:38–57.
   Web of Science ®Google Scholar
• Egorov YuV , Kondratiev VA . On spectral theory of elliptic operators. Basel: Birkhauser; 1996.
   Google Scholar
• Kondrat’ev VA , Oleinik OA . Boundary value problems for the system of elasticity theory in unbounded domains. Korn’s inequalities. Russian Math Surv. 1988;43(5):65–119.
   Web of Science ®Google Scholar
• Kondratiev VA , Oleinik OA . Hardy’s and Korn’s inequality and their application. Rend Mat Appl Serie VII. 1990;10(3):641–666.
   Google Scholar
• Kon’kov AA . On the dimension of the solution space of elliptic systems in unbounded domains. Russian Acad Sci Sbornik Math. 1995;80(2):411–434.
   Web of Science ®Google Scholar
• Matevosyan OA . On the uniqueness of the solution of the second boundary value problem for a system in elasticity theory for unbounded domains. Moscow Univ Math Bull. 1994;49(6):44–46.
   Google Scholar
• Matevosyan OA . On solutions of boundary value problems for a system in the theory of elasticity and for the biharmonic equation in a half-space. Diff Equ. 1998;34(6):803–808.
   Web of Science ®Google Scholar
• Matevosyan OA . The exterior Dirichlet problem for the biharmonic equation: solutions with bounded Dirichlet integral. Math Notes. 2001;70(3):363–377.
   Web of Science ®Google Scholar
• Matevossian OA . Solutions of exterior boundary value problems for the elasticity system in weighted spaces. Sbornik Math. 2001;192(12):1763–1798.
   Web of Science ®Google Scholar
• Matevossian HA . On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains. P-Adic Numbers Ultrametric Anal Appl. 2015;7(1):74–78.
   Web of Science ®Google Scholar
• Matevossian OA . On solutions of the Neumann problem for the biharmonic equation in unbounded domains. Math Notes. 2015;98:990–994.
   Web of Science ®Google Scholar
• Matevosyan OA . On solutions of the mixed Dirichlet--Navier problem for the polyharmonic equation in exterior domains. Russian J Math Phys. 2016;23(1):135–138.
   Web of Science ®Google Scholar
• Matevosyan OA . On solutions of one boundary value problem for the biharmonic equation. Diff Equ. 2016;52(10):1379–1383.
   Web of Science ®Google Scholar
• Matevossian HA . On the biharmonic Steklov problem in weighted spaces. Russian J Math Phys. 2017;24(1):134–138.
   Web of Science ®Google Scholar
• Matevossian HA . On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains. P-Adic Numbers Ultrametric Anal Appl. 2017;9(2):151–157.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Kondratiev VA , Oleinik OA . On the behavior at infinity of solutions of elliptic systems with a finite energy integral. Arch Rational Mech Anal. 1987;99(1):75–99.
   Web of Science ®Google Scholar
• Douglis A , Nirenberg L . Interior estimates for elliptic systems of partial differential equations. Commun Pure Appl Math. 1955;8:503–538.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Morrey CB . Multiple integrals in the calculus variations. Berlin: Springer-Verlag; 1966.
   Google Scholar