Stability results for some nonlinear elliptic equations involving the -laplacian with critical Sobolev growth
Stability results for some nonlinear elliptic equations involving the -Laplacian with critical Sobolev growth
This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the -Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the...
Optimal transportation for the determinant
Among -valued triples of random vectors having fixed marginal probability laws, what is the best way to jointly draw in such a way that the simplex generated by has maximal average volume? Motivated by this simple question, we study optimal transportation problems with several marginals when the objective function is the determinant or its absolute value.
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