论文标题
椭圆形均匀线性方程的Lebesgue可溶解度的注释
A note on Lebesgue solvability of elliptic homogeneous linear equations with measure data
论文作者
论文摘要
在这项工作中，我们为方程$ a^{*}（d）f =μ$ for $ f \ in l^{p} $和阳性度量数据$μ$与椭圆均匀的线性差异操作员$ $ $ a（d）$ m。我们的方法基于$（m，p） - $ $ $ $的能量控制，当$ 1 \ leq p <\ infty $时提供自然表征。我们还使用{新的$ l^{1} $估算椭圆机和取消操作员的措施估算了限制案例$ p = \ infty $在限制案例中获得足够的条件。
In this work, we present new results on solvability of the equation $A^{*}(D)f=μ$ for $f \in L^{p}$ and positive measure data $μ$ associated to an elliptic homogeneous linear differential operator $A(D)$ of order m. Our method is based on $(m,p)-$energy control of $μ$ giving a natural characterization for solutions when $1\leq p < \infty$. We also obtain sufficient conditions in the limiting case $p=\infty$ using {new $L^{1}$ estimates on measures for elliptic and canceling operators.
