## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Evolution Equations & Control Theory
- Foundations of Data Science
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- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
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- Journal of Modern Dynamics
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- AIMS Mathematics
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### Open Access Journals

DCDS

In this paper, we study the regularity of convex solutions to the Dirichlet problem
of the homogeneous Monge-Ampère equation $\det D^2 u=0$.
We prove that if the domain is a strip region and the boundary functions
are locally uniformly convex and $C^{k+2,\alpha}$ smooth,
then the solution is $C^{k+2,\alpha}$ smooth up to boundary.
By an example, we show the solution may fail to be $C^{2}$ smooth
if boundary functions are not locally uniformly convex.
Similar results have also been obtained for the Dirichlet problem
on bounded convex domains.

DCDS

In this paper we study partial and anisotropic Schauder estimates
for linear and nonlinear elliptic equations. We prove that if the
inhomogeneous term $f$ is Hölder continuous in the
$x_n$-direction, then the mixed derivatives u

_{xxn}are Hölder continuous; if $f$ satisfies an anisotropic Hölder continuity condition, then the second derivatives $D^2 u$ satisfy related anisotropic Hölder continuity estimates.
DCDS

This paper treats quasilinear elliptic equations in
divergence form whose inhomogeneous term is a signed measure. We
first prove the existence and continuity of generalized solutions to
the Dirichlet problem. The main result of this paper is a weak
convergence result, extending previous work of the authors for
subharmonic functions and non-negative measures. We also prove a
uniqueness result for uniformly elliptic operators and for operators
of $p$-Laplacian type.

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