Seminario

Seminario Análisis y EDPs

On asymptotic expansions and approximation schemes for the p-Laplacian

Ponente:  Félix del Teso (Universidad Complutense de Madrid)
Fecha:  miércoles 27 de octubre de 2021 - 15:00
Lugar:  Online - us06web.zoom.us/j/81491079139?pwd=OWo1TWc0NEExNDJZUFljWVRIdkZRQT09 (ID: 814 9107 9139; Access code: 937701)

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).