Measurable solutions for elliptic and evolution inclusions

Kenneth Kuttler

doi:10.3934/eect.2020041

Article Contents

2020, Volume 9, Issue 4: 1041-1055. Doi: 10.3934/eect.2020041

This issue Previous Article Relaxation of optimal control problems driven by nonlinear evolution equations Next Article Differential inclusion problems with convolution and discontinuous nonlinearities

Measurable solutions for elliptic and evolution inclusions

Kenneth Kuttler^,

249 Havenside Court, Grantsville, Utah 84029, USA

^* Kenneth Kuttler
^* Kenneth Kuttler

I would like to thank the anonymous referees for finding some loose ends and things which needed improvement.

Received: July 31, 2019

Revised: November 30, 2019

Early access: March 2020

Published: December 2020

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Abstract

This paper obtains existence of random variable solutions to elliptic and evolution inclusions. As a special case, surprising theorems are obtained for the quasistatic problems. A new existence theorem is also presented for evolution inclusions with set valued operators dependent on elements of a measurable space.

Keywords:

Measurable quasistatic inclusions,
measurable evolution inclusions.

Mathematics Subject Classification: Primary: 35R60; Secondary: 35Q74, 60H25.

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References

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