Limit Cases of the p-Laplace Operator via Mosco Convergence

Shen, Xiao

Student Work

Limit Cases of the p-Laplace Operator via Mosco Convergence

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In the classic theory, p-Laplace operator (1 < p < infinity) joined several main parts of the mathematics in a fruitful way, and one important principle of mathematics is that extreme cases reveal interesting structure. Looking at p-Laplace operator as subgradients of a sequence of convex functionals Ep, as p goes to 1 and to infinity, we study the connection of the dual problem between 1-Laplace operator and infinity-Laplace operator using tools from convex analysis and the notion of Mosco convergence.

This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

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