| Abstract: |
| We will discuss regularity issues regarding the weak solutions to non-homogeneous conormal derivative problem for quasilinear divergence form elliptic equations modeled on the $m$-Laplacian operator. The nonlinear terms are given by Carath\`{e}odory functions and satisfy controlled growth structure conditions with respect to the solution and its gradient, while their $x$-behaviour is controlled in terms of suitable Morrey spaces.
Global boundedness up to the boundary will be shown for the weak solutions of such equations, generalizing this way the classical $L^p$-result of Ladyzhenskaya and Ural`tseva to the framework of the Morrey scales. |
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