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Regularity of Lipschitz Solutions to the Minimal Surface Equation

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If you have a question about this talk, please contact Damon Civin .

It is well-known that a Lipschitz weak solution of the Minimal Surface Equation (MSE) is smooth in the interior of the domain. Usually, a lot of work (called De Giorgi-Nash-Moser Theory) goes into establishing the Holder continuity of the first derivatives, after which general principles from the theory of linear PDE take over and guarantee smoothness.

Drawing inspiration from techniques in geometric measure theory, one is able to, in the case of the MSE , devise an alternative approach to establishing the Holder continuity of the first derivatives which is completely expressible in the language of PDE but which avoids De Giorgi-Nash-Moser theory. I will outline this method, focussing on the geometry of the techniques.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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