Spectral stability for the perydinamic fractional $p$-Laplacian

Abstract

In this work we analyze the behavior of the spectrum of the peridynamic fractional $p$-Laplacian, $(-{\Delta }_p{)}_{\delta }^s$, under the limit process $\delta \to 0^{+}$ or $\delta \to +\infty$. We prove spectral convergence to the classical $p$-Laplacian under a suitable scaling as $\delta \to 0^{+}$ and to the fractional $p$-Laplacian as $\delta \to +\infty$.

References in corpus (1)

• Fractional p-eigenvalues