Research Interests

My research integrates analytic and geometric techniques to study partial differential equations. In particular my research investigates global/finite-in-time existence and stability results to geometric equations that model wave-like phenomena (i.e., relativistic membranes).

I am also working on regularity theory for the real Monge-Ampère equation with hopeful applications to generated Jacobian equations.

Selected Publications

• L. Abbrescia, W. Wong. "Global large data solutions of the membrane equation." In preparation.  
• L. Abbrescia. "Global Existence to Convolution-Type Vlasov Equations." In preparation.  
• L. Abbrescia, I. Huq-Kuruvilla, J. Nelson, N. Sultani. "Reeb Dynamics of the Link of the $A_n$ Singularity." Involve Vol. 10 (2017), No. 3, 417-442.  Open