NON-QUASIELLIPTIC BOUNDARY-VALUE PROBLEMS IN A CYLINDER WITH REGULARLY DEGENERATE MODEL PROBLEM ON THE CROSS-SECTION

S. A. Nazarov

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NON-QUASIELLIPTIC BOUNDARY-VALUE PROBLEMS IN A CYLINDER WITH REGULARLY DEGENERATE MODEL PROBLEM ON THE CROSS-SECTION

机译：截面上具有简并退化模型问题的圆柱体中的非拟椭圆型边值问题

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The author introduces a class of boundary-value problems in cylindrical domains. These problems are neither elliptic, nor parabolic, nor quasielliptic, but their main properties are inherited from problems of the said three types, namely, in a proper scale of weighted functional spaces, the operators of these problems are of Fredholm type and their solutions admit asymptotic expansions at infinity with power-exponential terms. The proof is based on precise estimates of solutions of some regularly degenerate model problems on the cross-section of the cylinder in stepwise norms depending on a small parameter.

机译：作者介绍了圆柱域中的一类边值问题。这些问题既不是椭圆形的，也不是抛物线形的，也不是拟椭圆形的，但是它们的主要性质是从上述三种类型的问题继承的，即在适当范围的加权函数空间中，这些问题的算子是Fredholm类型的，并且它们的解都允许幂指数项在无穷远处的渐近展开。该证明是基于对圆柱体横截面上一些规则退化模型问题的解的精确估计，并根据一个小参数以逐步范数进行逐步规范化。

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《Journal of Mathematical Sciences》 |2011年第4期|p.515-536|共22页
作者
S. A. Nazarov;
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作者单位

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia;

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NON-QUASIELLIPTIC BOUNDARY-VALUE PROBLEMS IN A CYLINDER WITH REGULARLY DEGENERATE MODEL PROBLEM ON THE CROSS-SECTION

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