Variational formulation of higher order elliptic boundary value problems
1983 ◽
Vol 28
(1)
◽
pp. 135-150
Keyword(s):
A Priori
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Let A be an elliptic (partial) differential operator of order 2m on a compact manifold with boundary Г. Let B be a normal system of m differential boundary operators on Г. Assume all manifolds and coefficients are arbitrarily smooth. We construct sesquilinear forms J in terms of which there are equivalent variational formulations of the natural boundary value problems determined by A and B with solutions in Sobolev spaces HS (M), 0 < s < 2m. Such forms are also constructed for problems with mixed boundary conditions. The variational formulation permits localization of a priori estimates and the interchange of existence and uniqueness questions between the boundary value problem and an associated adjoint problem.
1966 ◽
Vol 62
(4)
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pp. 753-759
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2013 ◽
Vol 58
(9)
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pp. 1201-1213
1980 ◽
Vol 29
(1)
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pp. 1-13
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1978 ◽
Vol 21
(1)
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pp. 83-93
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2011 ◽
Vol 217
(18)
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pp. 7385-7390
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Keyword(s):
2005 ◽
Vol 309
(2)
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pp. 505-516
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2022 ◽
Vol 3
(1)
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1981 ◽
Vol 31
(1)
◽
pp. 92-113
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