We prove that minimizers for subcritical second-order Sobolev embeddings in the unit ball are unique, positive and radially symmetric. Since the proofs of the corresponding first-order results cannot be extended to the present situation, we apply new and recently developed techniques.
Ferrero, A., Gazzola, F., Weth, T. (2007). Positivity, symmetry and uniqueness for minimizers of second-order Sobolev inequalities. ANNALI DI MATEMATICA PURA ED APPLICATA, 186(4), 565-578 [10.1007/s10231-006-0019-9].
Positivity, symmetry and uniqueness for minimizers of second-order Sobolev inequalities
FERRERO, ALBERTO;
2007
Abstract
We prove that minimizers for subcritical second-order Sobolev embeddings in the unit ball are unique, positive and radially symmetric. Since the proofs of the corresponding first-order results cannot be extended to the present situation, we apply new and recently developed techniques.
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