Super and ultracontractive bounds for doubly nonlinear evolution equations
Super and ultracontractive bounds for doubly nonlinear evolution equations
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双非线性演化方程的超收缩界和超收缩界
DOI：
10.4171/rmi/451
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发表时间：
2006
影响因子：
1.2
通讯作者：
G. Grillo
中科院分区：
文献类型：
--
作者：
M. Bonforte;G. Grillo
本文利用最近在[15]，[21]中导出的包含p-能量泛函的对数Sobolev不等式，证明了与双非线性发展方程u· =？p（um）（其中m（p - 1）= 1）在任意欧氏区域上，齐次Dirichlet边界条件被假定.约束的形式为||u（吨）||q = C|| u0||休息吗？/ ts的任意r = q I [1，+8）和t > 0和指数s，？被证明是这种类型的边界的唯一可能性。
We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = ?p(um) (with m(p - 1) = 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q = C||u0||r? / ts for any r = q I [1,+8) and t > 0 and the exponents s, ? are shown to be the only possible for a bound of such type.