On Besov regularity of solutions to nonlinear elliptic partial differential equations

摘要

In this paper, we study the regularity of the solutions to nonlinear elliptic equations. In particular, we are interested in smoothness estimates in the specific scale (B^{alpha}_{tau}(L_{tau})), τ=(α/d+1/2)−1, of Besov spaces which determines the approximation order of adaptive and other nonlinear numerical approximation schemes with respect to the L 2-norm. We show that the Besov regularity is high enough to justify the use of adaptive schemes.