Special Session 108: Regularity in local versus nonlocal problems

Different assumptions in vectorial elliptic problems with a focus on the quasilinear case
Marta Macr\`i
University of L`Aquila
Italy
Co-Author(s):    
Abstract:
This talk presents several structural assumptions used to prove existence and regularity for vectorial elliptic systems. In nonlinear settings, Uhlenbeck-type conditions, Landes-type assumptions, and more recent componentwise coercivity are frequently employed. In the quasilinear case, however, such hypotheses force all off diagonal coefficients to vanish, effectively decoupling the system. To address genuinely quasilinear, non-diagonal systems, one often imposes conditions on the support of the off diagonal coefficients. As a specific example, an existence and regularity result will be discussed for a quasilinear elliptic system with a drift term.