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pro vyhledávání: '"Gazoulis, Dimitrios"'
Autor:
Gazoulis, Dimitrios
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 Alexandrov, Bekelman and Pucci. These inequalities can be extended for f
Externí odkaz:
http://arxiv.org/abs/2409.01858
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 curvature. Also, we provide a local splitting theorem when the inequality i
Externí odkaz:
http://arxiv.org/abs/2310.14943
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 is currently used in numerous physical and engineering problems. The
Externí odkaz:
http://arxiv.org/abs/2308.05423
Autor:
Gazoulis, Dimitrios
We introduce the notion of $ P -$functions for fully nonlinear equations and establish a general criterion for obtaining such quantities for this class of equations. Some applications are gradient bounds, De Giorgi-type properties of entire solutions
Externí odkaz:
http://arxiv.org/abs/2306.06497
Autor:
Gazoulis, Dimitrios
We study minimizers of the Allen-Cahn system. We consider the $ \varepsilon $-energy functional with Dirichlet values and we establish the $ \Gamma $-limit. The minimizers of the limiting functional are closely related to minimizing partitions of the
Externí odkaz:
http://arxiv.org/abs/2301.07458
A Relation of the Allen-Cahn equations and the Euler equations and applications of the Equipartition
Autor:
Gazoulis, Dimitrios
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 consequence, we obtain De Giorgi type results, that is, the level sets of en
Externí odkaz:
http://arxiv.org/abs/2203.13960
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 locally near their minima. The corresponding formal Euler-Lagrange equation
Externí odkaz:
http://arxiv.org/abs/2106.07274
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, $H^1(S) = 0$, are necessarily identically constant. We show this under the additiona
Externí odkaz:
http://arxiv.org/abs/1611.06166
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