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Elliptic Functional Differential Equations with Degenerations
Lobachevskii Journal of Mathematics Pub Date : 2020-07-27 , DOI: 10.1134/s199508022005011x
V. A. Popov

Abstract

This review is devoted to differential-difference equations with degeneration in a bounded domain \(Q\subset\mathbb{R}^{n}\) and applications (Kato conjecture, nonlocal boundary value problem). We consider differential-difference operators with degeneration of the second order and generalization to \(2m\)-order and the case where differential-difference operator contains several degenerate difference operators with degeneration. Generalized solutions of such equations may not belong even to the Sobolev space \(W^{1}_{2}(Q)\).


中文翻译:

退化的椭圆型泛函微分方程

摘要

这篇评论致力于有界域\(Q \ subset \ mathbb {R} ^ {n} \)中退化的微分-微分方程及其应用(Kato猜想,非局部边值问题)。我们考虑了具有二阶退化并推广到\(2m \)-阶的微分差分算子,以及微分差分算子包含多个具有退化的简并差分算子的情况。这样的方程的广义解甚至可能不属于Sobolev空间\(W ^ {1} _ {2}(Q)\)
更新日期:2020-07-27
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