Abstract

We study the Dirichlet eigenvalue problem Δu =λu in Ω, u|_dΩ=0 for open and bounded sets Ω in R^n. An analogous distributional problem is formulated using the Sobolev space H^1_0(Ω). Viewing the Laplacian as an operator on this space we construct a compact, symmetric, positive-definite, and bounded inverse which
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