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Peter Humphries
Peter Humphries
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What is the first eigenvalue of $p$-LapacianLaplacian on unit sphere $S^n$?

We know that the first eigenvalue of Laplacian on the RiemannianRiemannian unit sphere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-Laplacian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

What is the first eigenvalue of $p$-Lapacian on unit sphere $S^n$?

We know that the first eigenvalue of Laplacian on the Riemannian unit sphere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-Laplacian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

What is the first eigenvalue of $p$-Laplacian on unit sphere $S^n$?

We know that the first eigenvalue of Laplacian on the Riemannian unit sphere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-Laplacian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

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Willie Wong
Willie Wong
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LaTeX the title and correct the spelling
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edit approved Oct 30, 2014 at 13:22
Paul
edit approved Oct 30, 2014 at 13:22
Paul
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what What is the first eigenvalue of p$p$-Lapacian on unit sphere S^n$S^n$?

weWe know that the first eigenvalue of Laplacian on the Riemannian unit shperesphere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-LapalcianLaplacian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

what is the first eigenvalue of p-Lapacian on unit sphere S^n?

we know that the first eigenvalue of Laplacian on the Riemannian unit shpere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-Lapalcian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

What is the first eigenvalue of $p$-Lapacian on unit sphere $S^n$?

We know that the first eigenvalue of Laplacian on the Riemannian unit sphere $S^n$ is $n$, then what is the explicit expression for the first eigenvalue of $p$-Laplacian on $S^n$?

The $p$-Laplacian eigevalue equation is $-div(|\nabla u|^{p-2}\nabla u)=\lambda| u|^{p-2}u$, for any $p>1$.

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mathsnail
mathsnail
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