UBC Math Harmonic Analysis Seminar: Scott Rodney

Abstract: In this talk I will discuss recent existence results for weak solutions to boundary value problems for matrix weighted degenerate elliptic PDEs with careful emphasis on special hypotheses. The PDEs under study have a principal part given by a matrix weighted $p$-Laplacian. During this journey, I will carefully develop the matrix weighted Sobolev spaces $QH1,p(v,Ω)$ for $1≤p≤∞$, and related Sobolev and Poincar\'e inequalities needed for an axiomatic development of the problem. If time permits, I will discuss recent results that produce the Sobolev and Poincar\'e inequalities used in our existence results.

All results discussed are joint with D. Cruz-Uribe (University of Alabama), F. Dal (Yildiz University, Turkiye), and S. Cetin (Istanbul Gelisim University, Turkiye)