论文标题
非抛物线形式的抛物线方程的单数解决方案
Singular solutions to parabolic equations in nondivergence form
论文作者
论文摘要
对于（0,1）$中的任何$α\，我们在两个空间尺寸中具有可测量系数的抛物线方程的解决方案的示例，该方程具有孤立的奇异性，并且不比$ c^α$更好。我们证明，在任何维度上都没有解决完全非线性的抛物线方程的解决方案，该方程在任何方面都具有孤立的奇异性，而在其他地方进行分析时，它不是$ c^2 $，并且在奇异时的$ x $中是均一的。我们为具有孤立的奇异性的完全非线性抛物线方程式建立了一个非均匀解决方案的示例，我们借助数值计算来验证。
For any $α\in (0,1)$, we construct an example of a solution to a parabolic equation with measurable coefficients in two space dimensions which has an isolated singularity and is not better that $C^α$. We prove that there exists no solution to a fully nonlinear uniformly parabolic equation, in any dimension, which has an isolated singularity where it is not $C^2$ while it is analytic elsewhere, and it is homogeneous in $x$ at the time of the singularity. We build an example of a non homogeneous solution to a fully nonlinear uniformly parabolic equation with an isolated singularity, which we verify with the aid of a numerical computation.
