5 papers
Eigenvalue Inequalities for Fully Nonlinear Elliptic Equations via the Alexandroff-Bakelman-Pucci Method
Dimitrios Gazoulis
In this work we establish eigenvalue inequalities for elliptic differential operators either for Dirichlet or for Robin eigenvalue problems, by using the technique introduced by Al…
Gradient Bounds and Liouville theorems for Quasi-linear equations on compact Manifolds with nonnegative Ricci curvature
Dimitrios Gazoulis, George Zacharopoulos
In this work we establish a gradient bound and Liouville-type theorems for solutions to Quasi-linear elliptic equations on compact Riemannian Manifolds with nonnegative Ricci curva…
On the Stability and Convergence of Physics Informed Neural Networks
Dimitrios Gazoulis, Ioannis Gkanis, Charalambos G. Makridakis
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and…
Applications of P-functions to Fully Nonlinear Elliptic equations: Gradient Estimates and Rigidity Results
Dimitrios Gazoulis
We introduce the notion of functions for fully nonlinear equations and establish a general criterion for obtaining such quantities for this class of equations. Some applicati…
Entire minimizers of Allen-Cahn systems with sub-quadratic potentials
Nicholas D. Alikakos, Dimitrios Gazoulis, Arghir Zarnescu
We study entire minimizers of the Allen-Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour local…