Linear Elliptic PDEs

Dear Colleagues,

Although the field of linear elliptical partial differential equations (PDEs) is one of the most-studied and best-understood topics in PDE theory and numerics; active research is still ongoing in this area. Regarding the analysis of linear elliptic operators, many open scientific problems can be found, e.g., in Section 5 of Vladimir Maz’ya, “Seventy Five (Thousand) Unsolved Problems in Analysis and Partial Differential Equations”, Integr. Equ. Oper. Theory (2018) 90:25, https://doi.org/10.1007/s00020-018-2460-8.

Among other things, new theoretical results about (systems of) linear elliptic PDEs and the regularity of solutions (for measure data or rough data) are suitable for this Special Issue. Furthermore, the numerical analysis of computational methods for the solution of linear elliptic PDEs (the finite element method, FEM; the finite difference method, FDM; and the finite volume method, FVM) and new trends in numerics, e.g., estimating Green’s function of a linear elliptic operator by machine learning or quantum algorithms for the solution of linear PDEs, fit into the scope of this Special Issue.

To summarize, this Special Issue gives authors the opportunity to present their latest findings related to linear elliptic PDEs.

Prof. Dr. Jochen Merker
Dr. Falko Baustian
Guest Editors

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