弾性論のDirichlet問題について

概要

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Let G be a bounded domain in R^p, G^^- its closure, and we assume that the boundary ∂G of G is piecewise smooth. Let D be a linear space of the whole of C^2 (G) functions which vanish on ∂G. We define the mapping A from D to L_2 (G) as follows: [numerical formula] where λ and μ stand for Lame's constants. By using the inner product ( , ) in L_2 (G), we define the inner product [ , ] on D as follows: [numerical formula] Let H_A be a completion of D, 〓・〓_A the norm in H_A・If there exists a element u_0∈H_A such that the functional [numerical formula] retains its minimum value for f∈L_2 (G), it may be said that the element u_0 is a generalized solution of Dirichlet problem in elasticity. In this note we established the existence and uniqueness of generalized solution in the above sense.
明治大学の論文