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Absolute continuity in partial differential equations. (English) Zbl 1384.28019

Summary: In this note, we study a function which frequently appears in partial differential equations. We prove that this function is absolutely continuous; hence it can be written as a definite integral. As a result, we obtain some estimates regarding solutions of the Hamilton-Jacobi systems.

MSC:

28D05 Measure-preserving transformations
35F21 Hamilton-Jacobi equations
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