On the biharmonic Steklov problem in weighted spaces
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S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. I,” Comm. Pure Appl. Math. 12 (4), 623–727 (1959).
F. Brock, “An Isoperimetric Inequality for Eigenvalues of the Stekloff Problem,” Z. Angew. Math. Mech. (ZAMM) 81 (1), 69–71 (2001).
D. Bucur, A. Ferrero, and F. Gazzola, “On the First Eigenvalue of a Fourth Order Steklov Problem,” Calc. Var. Partial Differential Equations 35 (1), 103–131 (2009).
D. Bucur and F. Gazzola, “The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization,” Milan J. Math. 79 (1), 247–258 (2011).
A. Douglis and L. Nirenberg, “Interior Estimates for Elliptic Systems of Partial Differential Equations,” Comm. Pure Appl. Math. 8 (4), 503–538 (1955).
Yu. V. Egorov and V. A. Kondratiev, On Spectral Theory of Elliptic Operators (Basel: Birkhauser, 1996).
R. Farwig, “A Note on the Reflection Principle for the Biharmonic Equation and the Stokes System,” Acta Appl. Math. 34 (1–2), 41–51 (1994).
F. Gazzola and G. Sweers, “On Positivity for the Biharmonic Operator under Steklov Boundary Conditions,” Arch. Ration Mech. Anal. 188 (3), 399–427 (2008).
F. Gazzola, H.-Ch. Grunau, and G. Sweers, Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains (Lecture Notes in Math. 1991, Springer, 2010).
V. A. Kondratiev and O. A. Oleinik, “On the Behavior at Infinity of Solutions of Elliptic Systems with a Finite Energy Integral,” Arch. Ration Mech. Anal. 99 (1), 75–99 (1987).
V. A. Kondratiev and O. A. Oleinik, “Boundary Value Problems for the System of Elasticity Theory in Unbounded Domains. Korn’s Inequalities,” Russ. Math. Surveys 43 (5), 65–119 (1988).
V. A. Kondratiev and O. A. Oleinik, “Hardy’s and Korn’s Inequality and Their Application,” Rend. Mat. Appl. Serie VII 10, 641–666 (1990).
A. A. Kon’kov, “On the Dimension of the Solution Space of Elliptic Systems in Unbounded Domains,” Russ. Acad. Sci. Sbornik Math. 80 (2), 411–434 (1995).
J. R. Kuttler and V. G. Sigillito, “Inequalities for Membrane and Stekloff Eigenvalues,” J. Math. Anal. Appl. 23 (1), 148–160 (1968).
O. A. Matevosyan, “On Solutions of Boundary Value Problems for a System in the Theory of Elasticity and for the Biharmonic Equation in a Half-Space,” Diff. Equations, 34 (6), 803–808 (1998).
O. A. Matevosyan, “The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral,” Math. Notes 70 (3), 363–377 (2001).
H. A. Matevossian, “On Solutions of Mixed Boundary Value Problems for the Elasticity System in Unbounded Domains,” Izvestiya Math. 67 (5), 895–929 (2003).
O. A. Matevosyan, “On Solutions of a Boundary Value Problem for a Polyharmonic Equation in Unbounded Domains,” Russian J. Math. Physics 21 (1), 130–132 (2014).
O. A. Matevosyan, “Solution of a Mixed Boundary Value Problem for the Biharmonic Equation with Finite Weighted Dirichlet Integral,” Diff. Equations 51 (4), 487–501 (2015).
O. A. Matevossian, “On Solutions of the Neumann Problem for the Biharmonic Equation in Unbounded Domains,” Math. Notes 98 (6), 990–994 (2015).
O. A. Matevosyan, “On Solutions of the Mixed Dirichlet–Navier Problem for the Polyharmonic Equation in Exterior Domains,” Russ. J. Math. Phys. 23 (1), 135–138 (2016).
O. A. Matevosyan, “On Solutions of One Boundary Value Problem for the Biharmonic Equation,” Differ. Equation, 52 (10), 1379–1383 (2016).
L. E. Payne, “Some Isoperimetric Inequalities for Harmonic Functions,” SIAM J. Math. Anal. 1 (3), 354–359 (1970).
S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics (3rd ed. Nauka, Moscow 1988); Applications of Functional Analysis in Mathematical Physics (AMS Providence 1991).
W. Stekloff, Sur les problèmes fondamentaux de la physique mathématique, Ann. Sci. de ècole. Norm. Sup. Ser. 3 19 (1902), 191–259 et 455–490.