论文标题
具有单数漂移的椭圆方程的基本解决方案
The Fundamental Solution of an Elliptic Equation with Singular Drift
论文作者
论文摘要
对于$ n \ geq 3 $，我们研究了椭圆形运算符的基本解决方案的存在和渐近特性，以非胶水形式，$ {\ nathcal l}（x，x，x，\ partial_x）= a_ {ij {ij}（ij}（ij}（x）\ partial_i \ partial_i \ partial_j+partial_j+b_k $ a $允许$ r^{ - 1}ω（r）$的连续性$ω（r）$满足方形条件和$ b_k $。引入了一个奇异的积分，以控制基本解决方案的存在。 We give examples that show the singular drift $b_k\partial_k$ may act as a perturbation that does not dramatically change the fundamental solution of ${\mathcal L}^o=a_{ij}\partial_i\partial_j$, or it could change an operator ${\mathcal L}^o$ that does not have a fundamental solution to one that does.
For $n\geq 3$, we study the existence and asymptotic properties of the fundamental solution for elliptic operators in nondivergence form, ${\mathcal L}(x,\partial_x)=a_{ij}(x)\partial_i\partial_j+b_k(x)\partial_k$, where the $a_{ij}$ have modulus of continuity $ω(r)$ satisfying the square-Dini condition and the $b_k$ are allowed mild singularities of order $r^{-1}ω(r)$. A singular integral is introduced that controls the existence of the fundamental solution. We give examples that show the singular drift $b_k\partial_k$ may act as a perturbation that does not dramatically change the fundamental solution of ${\mathcal L}^o=a_{ij}\partial_i\partial_j$, or it could change an operator ${\mathcal L}^o$ that does not have a fundamental solution to one that does.
