A Bridge between Sobolev and Escobar Inequalities and Beyond
نویسندگان
چکیده
The classical Sobolev and Escobar inequalities are embedded into the same oneparameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized for each inequality in this family by tweaking a well-known mass transportation argument. The case of the Dirichlet energy corresponds to a family of variational problems on conformally flat metrics, whose absolute minimizers interpolate between conformally flat elliptic and hyperbolic geometries, passing through the Euclidean geometry defined by the fundamental solution of the Laplacian.
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