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### Open Access Journals

CPAA

We establish local maximum principle for
$L^p$-viscosity solutions of fully nonlinear elliptic partial differential
equations with unbounded ingredients.

DCDS

We present an approach for proving uniqueness of ODEs in the Wasserstein space. We give an overview of basic tools needed to deal with Hamiltonian ODE in the Wasserstein space and show various continuity results for value functions. We discuss a concept of viscosity solutions of Hamilton-Jacobi equations in metric spaces and in some cases relate it to viscosity solutions in the sense of differentials in the Wasserstein space.

CPAA

Two results are proved in the paper. The first is a uniqueness theorem for
viscosity solutions of Dirichlet boundary value problems for
Bellman-Isaacs equations
with just measurable lower order terms. The second is a proof that
there always exist maximal and minimal viscosity solutions
of Dirichlet boundary value problems for fully nonlinear,
uniformly elliptic PDE that are measurable in the $x$-variable.

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