Abstract

In this note, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? The aim of the paper is twofold. Firstly, to give a survey of diverse examples on nonregular solutions to elliptic PDEs with emphasis on recent results on nonclassical solutions to fully nonlinear equations. Secondly, to define an appropriate algebraic formalism which makes the analytic part of the construction of nonclassical solutions more transparent.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call