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Limit Properties of Generalized Derivatives
Statement of the Problem of the Variational Calculus
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arbitrary assume Banach space belongs boundary conditions bounded called Chapter characteristic circle closed coefficients complete consequently consider const constant construct continuous converges coordinates corresponding defined denote depends derivatives differential equation Dirichlet problem domain eigenvalues element elliptic energy space equal to zero example exists expression fact follows formula function u(x given gives harmonic Hence holds homogeneous independent inequality infinite initial inside integral introduce limit linear matrix means method metric necessary Neumann problem norm normal obtain Obviously operator orthogonal posed positive definite possible potential properties prove quantity radius relation respect result satisfies segment sequence shown side solution space H sphere square-integrable sufficient Suppose surface term theorem transform uniformly uniqueness values variables variation wave equation write ди дх