Benjamin Jaye

Local and Global Behaviour of Solutions to Nonlinear Equations with Natural Growth Terms

AbstractIn this paper we study the Dirichlet problem

On the good- inequality for nonlinear potentials

\left\{\begin{array}{lll}-\Delta_p{u} = \sigma |u|^{p-2}u + \omega \quad {\rm in}\;\Omega,\\ u = 0 \qquad\quad\qquad\quad\;\qquad{\rm on}\;\partial\Omega,\end{array}\right.

Quasilinear elliptic equations and weighted Sobolev-Poincare inequalities with distributional weights

, where σ and ω are nonnegative Borel measures, and

The fundamental solution of nonlinear equations with natural growth terms

{\Delta_p{u} = \nabla \cdot (\nabla{u} \, |\nabla{u}|^{p-2})}

Reflectionless measures for Calder\'on-Zygmund Operators I: Basic Theory

is the p-Laplacian. Here