For additional information see A. Alexandrou Himonas's Personal Page.

Research Interests

I am interested in the regularity of solutions to linear partial differential equations (PDE), and in the Cauchy problem for nonlinear evolution equations. My earlier work concentrated on the microlocal analytic regularity of the solutions to principal type PDE with analytic coefficients. More recently I am working on the regularity theory (analytic, smooth) for degenerate elliptic PDE, in particular PDE that are sums of squares of vector fields. On non-linear PDE I am working on the well-posedness of the initial value problem for evolution equations.

Selected Publications

• J. Gorsky and A. Himonas; Construction of non-analytic solutions for the
  generalized KdV equation, to appear in Journal of Mathematical Analysis and Applications
• A. Himonas and G. Misiolek; Analyticity of the Cauchy problem for an integrable evolution equation,Math. Ann. 327, no. 3, 2003, 575--584
• A. Himonas and G.; Petronilho; Propagation of regularity and global Hypoellipticity, Michigan Math. J. 50, no. 3, 2002, 471--481
• A. Himonas and G. Misiolek; The Cauchy problem for an integrable shallow water equation, Differential and Integral Equations, 14, no.7, 2001, 821--831

Please direct questions and comments to: Alex.A.Himonas.1@nd.edu