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John Andersson: Viscosity solutions, the how and why of a mathematical generalization

Time: Wed 2014-09-17 15.15 - 16.15

Location: Room 3721, Lindstedtsvägen 25, 7th floor, Department of mathematics, KTH

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Generalizations are important in mathematics and one of the most fruitful generalizations in the area of partial differential equations is the concept of viscosity solutions. By defining a viscosity solution we extend the concept of the solution to a partial differential equation to functions that are not even differentiable.

How is this even possible to do in a reasonable way? Why would we want to define such solutions?

In this talk we will describe why viscosity solutions are important. And how it is possible to define a function u(x) that is merely continuous to be a solution to an equation involving second derivatives.

The talk will be directed to a general audience.