Convex duality for principal frequencies.

We consider the sharp Sobolev-Poincar\'e constant for the embedding of $W^{1,2}_0(\Omega)$ into $L^q(\Omega)$. We show that such a constant exhibits an unexpected dual variational formulation, in the range $1

Keywords:

• Range (mathematics)
• Convex optimization
• order
• Eigenvalues and eigenvectors
• Mathematics
• constraint
• Pure mathematics
• constant
• Embedding
• Omega

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