Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains
Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains
复制标题
非柱域抛物方程初始Lp狄利克雷问题的摄动与可解性
DOI：
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发表时间：
2014
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通讯作者：
J. Rivera
中科院分区：
文献类型：
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作者：
J. Rivera
对于二阶散度型抛物线性算子L，证明了在适当的小扰动下，初始Dirichlet问题在整个值域1，<1，p，<1，infty下的可解性.我们还证明了，如果L的系数满足Carleson测度条件形式的适当的受控振荡，则对于一定的p\，>\，1 $，非圆柱区域上与Lu\，=\，0 $相关的初始Dirichlet问题是可解的.所得结果是椭圆型方程相应结果的适当改进。
Abstract For parabolic linear operators $L$ of second order in divergence form, we prove that the solvability of initial ${{L}^{p}}$ Dirichlet problems for the whole range $1\,<\,p\,<\,\infty $ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of $L$ satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of $p\,>\,1$ , the initial ${{L}^{p}}$ Dirichlet problem associated with $Lu\,=\,0$ over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.