Abstract. Sufficient conditions for the existence and uniqueness of the solution of the Dirichlet problem of fourth order elliptic partial differential equations with variable coefficients have been derived. In a number of examples of practical interest, the easy applicability of these results has been shown.1. Introduction. A large class of problems of mathematical physics lead to fourth order elliptic partial differential equations with variable coefficients, the equations of the bending problems of elastic-isotropic, orthotropic and anisotropic-plates with variable (or constant) thickness being very particular cases of the general problem considered here. Hence, it is necessary to find sufficient conditions for the existence and uniqueness of the solution of the Dirichlet problem of these equations in weak form. This paper contains new results in this direction.
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