In this thesis we study the $L^p$ Dirichlet problem for second order divergence-form operators having a BMO antisymmetric part. To be precise, for the divergence-form …
This dissertation is devoted to the study of inverse spectral problem of Hankel operators. It is well-known that spectral characteristics of a Hankel operator does …
In this thesis, we study Prandtl's boundary layer theory for 2D, stationary, incompressible Navier-Stokes flows posed on domains with boundaries. The boundary layer hypothesis posed …
We study the one-dimensional Gross-Pitaevskii equation, a cubic defocusing non-linear Schrodinger equation with nonvanishing boundary conditions. In particular we linearize around the dark solitons, which …
Chapter 1 presents joint work with Nikolaos Kapouleas and is concerned with constructions of new closed, embedded minimal surfaces in the round three sphere using …
In this thesis we study the relation between the boundedness of commutators of singular integrals and the function spaces of bounded mean oscillation (BMO) type …
This thesis presents two general constructions of minimal surfaces by PDE gluing methods carreid out in collaboration with my advisor Nicolaos Kapouleas. In the first …
This thesis deals with sharp weighted estimates for classical operators in harmonic analysis. In the first chapter we study sharp weighted estimates in terms of …
In this thesis, we investigate the stability properties of a variety of PDE models concerning fluid dynamics, including charged fluids (plasmas). The models which we …
The famous domino shuffling algorithm was invented to generate the domino tilings of the Aztec Diamond. Using the domino height function, we view the domino …
Solutions of reaction-diffusion systems exhibit a wide variety of patterns like spirals, stripes and Turing patterns. In particular, the Belousov-Zhabotinsky (BZ) reaction produces spiral patterns, …