Abstract:
We study the wedge of solutions of the inequality $A(u) \geqslant 0$, where $A$ is a linear elliptic operator of order $2m$ acting on functions \linebreak of $n$ variables. We establish interior estimates of the form $\|u; W_p^{2m-1}(\omega)\| \leqslant C(\omega,\Omega) \|u;L(\Omega)\|$ for the elements of this wedge, where $\omega$ is a compact subdomain of $\Omega$, $W_p^{2 m-1}(\omega)$ is the Sobolev space, $p (n-1)<n$, $L(\Omega)$ is the Lebesgue space of integrable functions, and the constant $C(\omega,\Omega)$ is independent of $u$.
Fulltext:
PDF file (561 kB)
