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3 Unbounded Operators
5 Definition of the Spaces WfO and tfUfi
43 other sections not shown
assume Banach space belonging boundary condition boundary value problems bounded domain Cauchy problem Cauchy's inequality Chapter closure coefficients compact completely continuous consider constant converge weakly convergence in L2(Q corresponding defined denote dense derivatives difference quotients difference schemes differential equations Dirichlet problem domain Q du/dx dx dt eigenfunctions eigenvalues elements u(x elliptic equations elliptic operators embedding energy equal equivalent example extension fact follows Fourier free term function u(x Galerkin's method Hilbert space holds hyperbolic equations initial-boundary value problems interpolations investigation limit linear Lp(Q method of finite norm obtain orthogonal parabolic equations points precompact problem 2.1 proof properties right-hand side scalar product self-adjoint sequence smooth functions solution u(x solutions uA subspace summable Theorem 7.1 theory uk(x unique solvability uniqueness theorem valid vanish vector verify vertices weak convergence zero