2009/12/02 by Frank Duzaar, Giuseppe Mingione
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Degenerate energy levels #Lipschitz continuity #Lipschitz domain #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Physics #Pure mathematics #math.AP #msc:35D10 #msc:35J70
paper · pdf · doi:10.1016/j.anihpc.2010.07.002
arxiv created 2009/12/02 · openalex publication_date 2010/07/22 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We start presenting an L∞ -gradient bound for solutions to non-homogeneous p -Laplacean type systems and equations, via suitable non-linear potentials of the right-hand side. Such a bound implies a Lorentz space characterization of Lipschitz regularity of solutions which surprisingly turns out to be independent of p , and that reveals to be the same classical one for the standard Laplacean operator. In turn, the a priori estimates derived imply the existence of locally Lipschitz regular solutions to certain degenerate systems with critical growth of the type arising when considering geometric analysis problems.