Rico Zacher
Core Contributions
Zacher is an authority on the regularity theory of fractional evolution equations. He has made systematic contributions to the De Giorgi-Nash type theorem for time-fractional diffusion equations, the weak Harnack inequality, and the boundedness of weak solutions under discontinuous coefficients, establishing profound regularity correspondences between fractional and classical parabolic equations.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 2005 | "Maximal regularity of type Lp for abstract parabolic Volterra equations" | Established the Lp maximal regularity theory for abstract parabolic Volterra equations, laying the analytical foundation for subsequent regularity studies of fractional equations |
| 2007 | "A weak Harnack inequality for fractional differential equations" | First established a weak Harnack inequality for fractional differential equations, proving the positivity and local boundedness of solutions |
| 2008 | "Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients" | Proved the boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients, breaking through the classical requirement of coefficient smoothness |
| 2009 | "Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces" | Established the existence and uniqueness theory for weak solutions of abstract evolutionary integro-differential equations in Hilbert space frameworks |
| 2011 | "The Harnack inequality for the Riemann-Liouville fractional derivation operator" | Established the Harnack inequality for the Riemann-Liouville fractional derivative operator, characterizing the lower bound estimates for solutions |
| 2012 | "Global strong solvability of a quasilinear subdiffusion problem" | Proved the existence of global strong solutions to a quasilinear subdiffusion problem, extending regularity theory to nonlinear fractional equations |
| 2013 | "A De Giorgi-Nash type theorem for time fractional diffusion equations" | Extended the classical De Giorgi-Nash theorem to time-fractional diffusion equations, proving the Holder continuity of solutions |
| 2013 | "A weak Harnack inequality for fractional evolution equations with discontinuous coefficients" | Established a weak Harnack inequality for fractional evolution equations with discontinuous coefficients, unifying the smooth and non-smooth coefficient cases |