Abstract

We study the Fredholm property of semielliptic operators in anisotropic weighted spaces in \(\mathbb{R}^{n}\). In this paper necessary conditions are obtained for fulfillment of a priori estimates for such operators. Necessary and sufficient conditions are obtained for the Fredholm property of semielliptic operators with variable coefficients that have certain rate at infinity.

中文翻译：

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$$\boldsymbol{\mathbb{R}}^{\boldsymbol{n}}$$中各向异性加权空间中半椭圆算子的Fredholm性质

摘要

我们研究了\(\mathbb{R}^{n}\)中各向异性加权空间中半椭圆算子的 Fredholm 性质。在本文中，获得了满足这些算子的先验估计的必要条件。得到了在无穷远处具有一定速率的变系数半椭圆算子的Fredholm性质的充要条件。