A general product measurability theorem with applications to variational inequalities
Date
2016-03-31
Authors
Kuttler, Kenneth
Li, Ji
Shillor, Meir
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.
Description
Keywords
Partial differential inclusions, Product measurability, Variational inequalities, Measurable selection
Citation
Kuttler, K. L., Li, J., & Shillor, M. (2016). A general product measurability theorem with applications to variational inequalities. <i>Electronic Journal of Differential Equations, 2016</i>(90), pp. 1-12.
Rights
Attribution 4.0 International