LOCAL REGULARITY OF SOLUTIONS OF SOBOLEV- GALPERN PARTIAL DIFFERENTIAL EQUATIONS
LOCAL REGULARITY OF SOLUTIONS OF SOBOLEV- GALPERN PARTIAL DIFFERENTIAL EQUATIONS
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Sobolev-Galpern偏微分方程解的局部正则性
DOI：
10.2140/pjm.1970.34.781
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发表时间：
1970
影响因子：
0.6
通讯作者：
R. Showalter
中科院分区：
文献类型：
--
作者：
R. Showalter
设M和L分别是2m阶和2/2阶椭圆型微分算子，mS，建立了抽象混合初边值问题Mu(T)+Lu(T)=0，u(0)=u0在强连续半群的无穷小生成元域中的解的存在唯一性.本文的目的是证明这个半群是全纯的，从而得到了解的可微性结果以及它对初始函数u0的收敛为110。
Let M and L be elliptic differential operators of orders 2m and 2/, respectively, with m S. The existence and uniqueness of a solution to the abstract mixed initial and boundary value problem Mu(t) + Lu(t) = 0, u(0) = u0 was established for u0 given in the domain of the infinitesimal generator of a strongly-continuous semi-group. The purpose of this paper is to show that this semi-group is holomorphic and then obtain differentiability results for the solution and convergence of this solution to the initial function u0 as 110.