- Agmon , S. , Douglis , A. and Nirenberg , L. 1959 . Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions . I. Comm. Pure Appl. Math. , 12 : 623 – 737 .
- Agmon , S. 1960 . Maximum theorems for solutions of higher order elliptic equations . Bull. Amer. Math. Soc. , 66 : 77 – 80 .
- Agmon , S. , Douglis , A. and Nirenberg , L. 1964 . Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions . II. Comm. Pure Appl. Math. , 17 : 35 – 92 .
- Cohn , D.L. 1997 . Measure Theory , Boston, Basel, Berlin : Birkhäuser .
- Diestel , J. and UhI , J.J. Jr. 1977 . Vector Measures. Mathematical Surveys, Number 15 , Providence : American Mathematical Society .
- Dunford , N. and Schwartz , J.T. 1988 . Linear Operators. Part I: General Theory , New York, Chichester, Brisbane, Toronto, Singapore : John Wiley and Sons .
- Kresin , G.I. and Maz'ya , V.G. 1988 . On the exact constant in a Miranda-Agmon type inequality for solutions of elliptic equations (Russian) . Izveslia Vys. Uch. Zaved.. Matem. Ser. , 5 : 41 – 50 .
- Izvestia VUZ. Matematika , 32 (5) 49 – 59 . English transi.
- Kresin , G.I. and Maz'ya , V.G. 1993 . Criteria for validity of the maximum modulus principle for solutions of linear strongly elliptic second order systems . Potential Analysis , 2 : 73 – 99 .
- Kresin , G.I. and Maz'ya , V.G. 2002 . Sharp parametric estimates for analytic and harmonic functions related to Hadamard-Borel-Caratheodory inequalities . Functional Differential Equations , 9 (1-2) (to appear)
- Kupradze , V.D. , Gegelia , T.G. , Basheleishvili , M.O. and Burchuladze , T.V. 1979 . Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , Amsterdam : North-Holland .
- Ladyzhenskaya , O.A. 1963 . The Mathematical Theory of Viscous Incompressible Flow , New York : Gordon and Breach .
- Lopatinskii , Ya.B. 1953 . On a method of reducing boundary value problems for systems of differential equations of elliptic type to regular integral equations (Russian) . Ukrain. Mat. Zumal , 5 (2) : 123 – 151 .
- Maz'ya , V.G. and Kresin , G.I. 1984 . On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients (Russian) . Matem. Sbornik , 125 (167) : 458 – 480 .
- 1986 . Math. USSR-Sb. , 53 : 457 – 479 . English transi.
- Miranda , C. 1958 . Teorema del massimo modulo e teorema di esistenza e di unicità per il problèma di Dirichlet relative alle equazioni ellitiche in due variabili . Ann. Mat. Pura Appl., Ser. , 4 (46) : 265 – 311 .
- Muskhelishvili , N.I. 1953 . Some Basic Problems of the Mathematical Theory of Elasticity , Groningen, Holland : Noordhoff .
- Shapiro , Z.Ya. 1951 . The first boundary value problem for an elliptic system of differential equations (Russian) . Mat. Sb. , 28 (70) : 55 – 78 .
- Solonnikov , V.A. 1964 . On general boundary value problems for systems elliptic in the Douglis-Nirenberg sense (Russian) . Izv. Akad. Nauk SSSR. ser. Mat. , 28 : 665 – 706 .
- 1966 . Amer. Math. Soc. Transi. , 2 ( 56 ) English transi
Best Constants in the Miranda-Agmon Inequalities for Solutions of Elliptic Systems and the Classical Maximum Modulus Principle for Fluid and Elastic Half-spaces
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