Abstract

In this paper we consider of a multidimensional loaded mixed type equation of the second order with some seminonlocal conditions on the coefficients. The existence and uniqueness of solution of the seminonlocal boundary value problem of second kind is proved in the Sobolev space \(W\ _{2}^{3}(Q)\). In proof of the theorems are used the methods of ‘‘\(\varepsilon\)-regularizations’’, a priori estimate and successive approximations.

中文翻译：

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关于第二类多维加载混合型方程的半非局部边值问题

摘要

在本文中，我们考虑了二阶多维加载混合型方程，并且在系数上存在一些半非局部条件。在Sobolev空间\（W \ _ {2} ^ {3}（Q）\）中证明了第二类半非局部边值问题解的存在性和唯一性。在定理的证明中使用了“ \（\ varepsilon \） -正则化”，先验估计和逐次逼近的方法。