Teixeira, Eduardo V. Regularity theory for nonlinear diffusion processes. (English) Zbl 1462.76176 Notices Am. Math. Soc. 67, No. 4, 475-482 (2020). The paper is a survey of results on diffusion equations and is an introductory material. The focus is on steady equations, which are elliptic. The author tells about the connection between elliptic equations and analytic functions, the mean properties, etc, and then passes to regularity results as a priori norm estimations. Then heterogeneous media are considered, with diffusivity being a tensor, and regularity results for this case are discussed. The rest of the paper is devoted to nonlinear elliptic PDEs, free boundary, and regularity of solutions of such problems. Reviewer: Ilya A. Chernov (Petrozavodsk) Cited in 5 Documents MSC: 76R50 Diffusion 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 35R35 Free boundary problems for PDEs Keywords:nonlinear elliptic equation; a priori estimate; free boundary problem PDFBibTeX XMLCite \textit{E. V. Teixeira}, Notices Am. Math. Soc. 67, No. 4, 475--482 (2020; Zbl 1462.76176) Full Text: DOI