4 papers · 1 filter
On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians
Pascal Auscher, Khalid Baadi
We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class , accompanied…
Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds
Khalid Baadi
In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatia…
On well-posedness for second-order degenerate parabolic equations with unbounded lower-order terms
Khalid Baadi
In this paper, we establish the well-posedness of Cauchy problems for weak solutions to second-order degenerate parabolic equations with a non-smooth, time-dependent degenerate ell…
Fundamental solutions for parabolic equations and systems: universal existence, uniqueness, representation
Pascal Auscher, Khalid Baadi
In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smoot…