Recent Developments in the Existence and Differentiability Theory of Elliptic Differential EquationsDepartment of Mathematics, University of California, 1956 - Differential equations, Partial - 120 pages |
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aªß absolute continuity analytic analytic function B₂ bªu bi-Lipschitz transformation boundary values C₂ Cauchy sequence Cauchy-Kowalewski theorem cell choose closure compact set completely continuous condition on G converges strongly converges weakly d₂ Definition 2.5 derivative differentiability domain G elements elliptic equation equivalent to f f belongs f in Lp(R F satisfies function defined function f functions of class G is Lipschitzian Gårding's lemma H₂ Hilbert space inequality inner product integral interior to G L₂ Let f linear transformation Lipschitz domain Lipschitzian domain Lp(G neighborhood norm open set partition of unity Poincaré's lemma proof of Theorem prove Pu(x R₁ R₂ result follows satisfies a uniform sequence f strongly to f subset Suppose Theorem 2.7 uniform Lipschitz condition vanishes identically variables weak convergence weakly to f α α αβ Σ Σ аха