论文标题
同质进化方程与扰动的正规化效应
Regularizing effect of homogeneous evolution equations with perturbation
论文作者
论文摘要
由于Aronson＆Bénilan的开创性作品[C. R. Acad。科学。巴黎Sér。，1979年]和Bénilan＆Crandall [Johns Hopkins Univ。出版社，1981年，众所周知，由非线性但均匀的操作员控制的一阶进化问题承认，平滑效果是，每种相应的轻度解决方案都是Lipschitz在每个正时的连续lipschitz。此外，如果基础的Banach空间具有ranikodým的特性，那么这些温和的解决方案为A.E.可差异，时间来源满足全球和点的界限。 在本文中，我们表明，如果同质运算符被Lipschitz连续映射扰动，这些结果仍然是正确的。更确切地说，我们建立了全球$ l^1 $ Aronson-Bénilan类型估计值，并确定Aronson-Bénilan类型估算。我们将我们的理论运用来得出全局$ l^q $ - $ l^{\ infty} $ - 估计由dirichlet到neumann操作员与$ p $ - laplace-beltrami操作员相关的扰动扩散问题的时间衍生，并在compact riemannianianianianianianianianianian centrical concercrandord carvistords anderolds corparitord carvistords and coptractectiond。
Since the pioneering works by Aronson & Bénilan [C. R. Acad. Sci. Paris Sér., 1979] and Bénilan & Crandall [Johns Hopkins Univ. Press, 1981], it is well-known that first-order evolution problems governed by a nonlinear but homogeneous operator admit the smoothing effect that every corresponding mild solution is Lipschitz continuous at every positive time. Moreover, if the underlying Banach space has the Radon-Nikodým property, then these mild solution is a.e. differentiable, and the time-derivative satisfies global and point-wise bounds. In this paper, we show that these results remain true if the homogeneous operator is perturbed by a Lipschitz continuous mapping. More precisely, we establish global $L^1$ Aronson-Bénilan type estimates and point-wise Aronson-Bénilan type estimates. We apply our theory to derive global $L^q$-$L^{\infty}$-estimates on the time-derivative of the perturbed diffusion problem governed by the Dirichlet-to-Neumann operator associated with the $p$-Laplace-Beltrami operator and lower-order terms on a compact Riemannian manifold with a Lipschitz boundary.
