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A-proper applying apriori estimates arbitrary assume assumptions asymptotic centre Banach space boundary value problems bounded domain Calculus of Variations Chap coefficients compact consider constant continuous convex set COROLLARY Czechoslovakia defined demicontinuous denote differentiable functions Dirichlet problem elliptic equations elliptic operators example exists fixed point function f GIAQUINTA GIUSTI Holder-continuous holds implies inequality infinitely differentiable L. C. EVANS Lemma linear elliptic M(Wm mappings methods minimum point mollifiers multiple integrals multipliers non-linear elliptic systems nonexpansive nonlinear nonlinear elliptic norm obtain open set P. L. Lions parabolic partial differential equations partition of unity proof of Theorem properties Proposition prove quasi-minima REMARK Russian satisfying the condition sequence Sobolev spaces solutions of elliptic solvability stationary points subset supp Theorem 1.1 theory tions topological uniformly V. G. MAZ'YA variable step vector viscosity solution weak solution