Semilinear Dirichlet problem for subordinate spectral Laplacian

Ivan Biočić

doi:10.3934/cpaa.2023012

Article Contents

2023, Volume 22, Issue 3: 851-898. Doi: 10.3934/cpaa.2023012

This issue Previous Article Global asymptotic stability of the rarefaction waves to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation laws Next Article Pointwise estimates for systems of coupled $ p $-Laplacian elliptic equations

Semilinear Dirichlet problem for subordinate spectral Laplacian

Ivan Biočić

Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia

Received: June 2022

Revised: November 2022

Early access: December 19, 2022

Published online: December 19, 2022

The author is supported in part by the Croatian Science Foundation under the project 4197.

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Abstract

We study semilinear problems in bounded $ C^{1, 1} $ domains for non-local operators with a boundary condition. The operators cover and extend the case of the spectral fractional Laplacian. We also study harmonic functions with respect to the non-local operator and boundary behaviour of Green and Poisson potentials.

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Mathematics Subject Classification: Primary: 35J61, 35R11; Secondary: 35C15, 31B10, 31B25, 31C05, 60J35.

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