Symmetry Problems on Stationary Isothermic Surfaces in Euclidean Spaces

Sakaguchi, Shigeru

doi:10.1007/978-3-319-41538-3_13

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The Squared Distance Function From the Boundary1

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2018

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“…The proof of Lemma 2.13 follows from [3, Theorem 3] and from the fact that d(x) = h − d 0 (x) (see also [37]). Now we are ready to state the following theorem concerning the eigenvalues of D 2 η.…”

Section: The Squared Distance Function From the Boundarymentioning

confidence: 99%

Weyl-type bounds for Steklov eigenvalues

Provenzano

Stubbe

2018

J. Spectr. Theory

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We present upper and lower bounds for Steklov eigenvalues for domains in R N +1 with C 2 boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key result is a comparison of Steklov eigenvalues and Laplacian eigenvalues on the boundary of the domain by applying Pohozaev-type identities on an appropriate tubular neigborhood of the boundary and the min-max principle. Asymptotically sharp bounds then follow from bounds for Riesz-means of Laplacian eigenvalues.

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Section: The Squared Distance Function From the Boundarymentioning

confidence: 99%