摘要
本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要.
The present paper concerns with the following semilinear degenerate elliptic equation
yΔu + aux + buy + cu = ε0F(x,y,u,ux,uy),
the author investigates the boundary value problems in a bounded periodic domain Ω, which is homeomorphic to the cylindrical surface. The well-posedness and regularity of the corresponding linear problems are dealed with by the elliptic regularization method. Based on the results above, the author obtains some results on the existence of solution to the above semilinear problems by Moser's lemma and Banach fixed point theorem. Such problems are very closely related to the rigidity problems arising from infinitesimal isometric deformation. And the regularity of solutions to such problems plays an Important role in the study of geometry problems.
出处
《数学年刊（A辑）》
CSCD
北大核心
2004年第2期225-242,共18页
Chinese Annals of Mathematics
关键词
退化半线性椭圆型方程
适定性
正则性
先验估计
Degenerate semilinear elliptic equation, Well-posedness, Regularity, Priori estimate
