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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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A priori estimate of an inhomogeneous p-Laplace equation with Dirichlet boundary condition
I'm currently working on this Dirichlet problem:
\begin{cases}
div(\sigma |\nabla u|^{p-2} \nabla u) = f &\quad {in }~ \Omega\\
u = g &\quad in~\partial\Omega
\end{cases}
with $\sigma \in L^{\infty …