We consider an elliptic PDE problem related with fluid mechanics. We show that level sets of rescaled solutions satisfy the zero mean curvature equation in a suitable weak viscosity sense. In particular, such level sets cannot be touched from below (above) by a convex (concave) paraboloid in a suitably small neighborhood.
Bernoulli jets and the zero mean curvature equation / E. Valdinoci. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 225:2(2006), pp. 710-736.
Bernoulli jets and the zero mean curvature equation
E. Valdinoci
2006
Abstract
We consider an elliptic PDE problem related with fluid mechanics. We show that level sets of rescaled solutions satisfy the zero mean curvature equation in a suitable weak viscosity sense. In particular, such level sets cannot be touched from below (above) by a convex (concave) paraboloid in a suitably small neighborhood.
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