The Dirichlet Problem for a Hyperbolic Equation

This paper deals with the Dirichlet problem for the hyperbolic differential equation (1) $${U_{xy}} = 0$$ i. e. with the problem of determining a solution u of (1) from given values on a closed curve C.1 Simple examples show that the Dirichlet problem for a hyperbolic equation has a completely different character from that of the corresponding problem for an elliptic equation such as the potential equation (2) $${U_{xx}} + {U_{yy}} = 0$$

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