Departamento de Matemáticas UAM

Online Analysis and PDE seminar (UAM-UC-UC3M-UCM-ICMAT-IMUS)

Ponente: Félix del Teso (U. Complutense de Madrid)

Fecha: Miércoles 27 de octubre de 2021 - 15:00

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Resumen: The aim of this talk is to introduce the topic of asymptotic expansions and approximation schemes for p-Laplacian type operators. We will present the results in collaboration with J. J. Manfredi and M. Parviainen ([3]). Here, we show a unified framework to prove convergence of approximation schemes for boundary value problems regarding normalized p-Laplacian, which has to be treated in the context of viscosity solutions. While for the normalized p-Laplacian, asymptotic expansion and finite difference discretizations were very well known, this was not the case for p-Laplapcian. In the second part of the talk, we will present such results. This is a work in collaboration with E. Lindgren ([1, 2]). Here, we introduce new asymptotic expansions and finite difference discretizations and show convergence of approximation schemes for associated problems.

 

References:

 

[1] del Teso, Felix; Lindgren, Erik; A mean value formula for the variational p-Laplacian. NoDEA Nonlinear Differential Equations Appl., 28 (2021), no. 3, Paper No. 27, 33 pp.
[2] del Teso, Felix; Lindgren, Erik; A finite difference method for the varia-tional p-Laplacian Preprint, https://arxiv.org/abs/2103.06945. (2021)
[3] del Teso, Felix; Manfredi, Juan J.; Parviainen, Mikko; Convergence of dynamic programming principles for the p-Laplacian. Advances in Calculus of Variations, Ahead of print. (2019).

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