The paper compiles known results, counter-examples, and open problems on critical values of the Dirichlet integral constrained to the L^q unit sphere as a generalization of Dirichlet eigenvalues.
Maz’ya, Sobolev spaces, Sobolev spaces with applications to elliptic partial differential equations
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An overview on constrained critical points of Dirichlet integrals
The paper compiles known results, counter-examples, and open problems on critical values of the Dirichlet integral constrained to the L^q unit sphere as a generalization of Dirichlet eigenvalues.