Research Interest


Stochastic Partial Differential Equations:

I have been working on the maximal L_p (or Sobolev)-regularity theory of SPDEs with the emphasis on the following:

  1. Differential operators: 2nd-order operators, pseudo-differential operators,  infinitesimal generator of Levy process, and operators related to  anomalous diffusions.
  2. Domains: C^1-domains, Lipschitz domains, angular domain and general non-smooth domains.
  3. Coefficients: continuous leading coefficients, measurable leading coefficients,  unbounded leading coefficients, and degenerate equations.
  4. Noises: Brownian motions, Levy noises, semi-martingales.
  5. Some quasi-and semi-linear SPDEs


2nd-oder Linear PDEs:

  1.  Discontinuous, degenerate and  unbounded leading coefficients.
  2. Weighted L_p-regularity theory on non-smooth domains.


PDE related to stochastic processes:

I also have great interest in L_p and H\"oder regularity theory for PDEs whose differential operators are infinitesimal generator of stochastic processes such as Levy processes and non-stationary stochastic processes.