Solving of Partial Differential Equations under Minimal Conditions

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2008
• Main Authors: Maslyuchenko, V.K., Mykhaylyuk, V.V.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106505
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Solving of Partial Differential Equations under Minimal Conditions / V.K. Maslyuchenko, V.V. Mykhaylyuk // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 252-266. — Бібліогр.: 7 назв. — англ.

It is proved that a differentiable with respect to each variable function f : R2 → R is a solution of the equation ∂u/∂x + ∂u/∂y = 0 if and only if there exists a function φ : R → R such that f(x, y) = φ(x - y). This gives a positive answer to a question by R. Baire. Besides, this result is used to...