论文标题
边界数据的边界价值问题
Boundary value problems with rough boundary data
论文作者
论文摘要
我们考虑了高阶参数 - 椭圆方程的线性边界值问题，其中边界数据不属于经典痕量空间。我们采用一类混合平滑度的Sobolev空间，该空间在负顺序的BESOV空间中接收了一个广义的边界迹线。我们证明了半空间和足够光滑的域中粗糙边界数据的独特解决性。作为一个应用程序，我们表明与线性化的Cahn--Hilliard方程相关的操作员与动态边界条件相关的是在$ l^p（\ Mathbb r^n _+）\ times l^p（\ Mathbb r^{n-1}）中生成全体形态半群。
We consider linear boundary value problems for higher-order parameter-elliptic equations, where the boundary data do not belong to the classical trace spaces. We employ a class of Sobolev spaces of mixed smoothness that admits a generalized boundary trace with values in Besov spaces of negative order. We prove unique solvability for rough boundary data in the half-space and in sufficiently smooth domains. As an application, we show that the operator related to the linearized Cahn--Hilliard equation with dynamic boundary conditions generates a holomorphic semigroup in $L^p(\mathbb R^n_+)\times L^p(\mathbb R^{n-1})$.
