论文标题
Quasilinear P.D.ES，插值空间和Hölderian映射
Quasilinear P.D.Es, Interpolation spaces and Hölderian mappings
论文作者
论文摘要
就像塔塔尔（Tartar）的工作一样（塔塔尔（Tartar L. L.）插值非上亚利亚（Noninéaire）等人，9，功能分析杂志，（1972年），第469-489页），我们在这里开发了一些新的结果，这些结果涉及$α$-hölderian映射的$α$-höldermappaces的非线性插值，是在常规的空间之间的互动之间的互动，即$ knterp in the $ k $ k $ k $ k $ k k.对数函数。我们将这些结果应用于解决方案的梯度上的规律性结果，以$ $$ -div（\ wideHat a（\ nabla u））+v（u）= f，$ v $是非线性潜力，$ f $ a $ f $ a以lorentz-zygmund space的非标准空间。我们还表明，在适当的值$α$的情况下，映射$ t：\ tf = \ nabla u $是本地或全球$α$-Hölderian，以及$ v $和$ \ widehat a的适当假设。
As in the work of Tartar ( Tartar L. Interpolation non linéaire et régularité, 9, Journal of Functional Analysis, (1972), 469-489) we developed here some new results on non linear interpolation of $α$-Hölderian mappings between normed spaces, namely, by studying the action of the mappings on $K$-functionals and between interpolation spaces with logarithm functors. We apply those results to obtain regularity results on the gradient of the solution to quasilinear equations of the form $$-div(\widehat a(\nabla u ))+V(u)=f, $$ whenever $V$ is a nonlinear potential, $f$ belongs to non standard spaces as Lorentz-Zygmund spaces. We show among other that the mapping $T: \ Tf=\nabla u$ is locally or globally $α$-Hölderian under suitable values of $α$ and adequate hypothesis on $V$ and $\widehat a.$
