Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
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For n at least 7 on positive manifolds with non-negative constant boundary mean curvature and a nonumbilic point, least-energy nodal solutions to the Yamabe boundary-value problem exist.
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Sign-changing solutions to the Yamabe problem on manifolds with boundary
For n at least 7 on positive manifolds with non-negative constant boundary mean curvature and a nonumbilic point, least-energy nodal solutions to the Yamabe boundary-value problem exist.