双调和型抛物方程的Schauder估计

Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type

该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性.类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性.该方法简单而易懂.

Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type were proved. The existence and uniqueness of the solutions in the suitable space were obtained. Similarly to the second-order case,a fornal expression of solutions by the Fourier transform was obtained. Then the regularity, uniqueness, existence of solutions using the potential theory and approximation argument were got. The approach is simple and straightforward.