3 citations · 4 across the 7 of their papers we have counts for
8 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…
On the -convergence of the Allen-Cahn functional with boundary conditions
Dimitrios Gazoulis
We study minimizers of the Allen-Cahn system. We consider the -energy functional with Dirichlet values and we establish the -limit. The minimizers of the limitin…
A Relation of the Allen-Cahn equations and the Euler equations and applications of the Equipartition
Dimitrios Gazoulis
We will prove that solutions of the Allen-Cahn equations that satisfy the equipartition can be transformed into solutions of the Euler equations with constant pressure. As a conseq…
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…
On Almost Entire Solutions Of The Burgers Equation
Nicholas Alikakos, Dimitrios Gazoulis
Solutions that satisfy classically the Burgers equation except, perhaps, on a closed set S of the plane of potential singularities whose Hausdorff 1-measure is zero, ,…