论文标题
抛物线方程在具有混合规范的Sobolev空间中具有无界低阶系数
Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms
论文作者
论文摘要
我们证明了LP，以完全低阶项为差异形式的抛物线方程的Q-可溶性。系数和非均匀术语属于最低的集成性条件的混合Lebesgue空间。特别是，低阶项的系数不一定是有限的。我们研究了不规则域上的dirichlet和吻合衍生物边界值问题。我们还证明了抛物线Sobolev空间的嵌入结果，其证明具有独立感兴趣。
We prove the Lp,q-solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with the lowest integrability conditions. In particular, the coefficients for the lower-order terms are not necessarily bounded. We study both the Dirichlet and conormal derivative boundary value problems on irregular domains. We also prove embedding results for parabolic Sobolev spaces, the proof of which is of independent interest.
