Heat-kernels and maximal Lp − Lq−estimates: the non-autonomous case
Hieber, Matthias ; Monniaux, Sylvie
HAL, hal-00535645 / Harvested from HAL
Text on HAL
In this paper, we establish maximal Lp−Lq estimates for non autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators −A(t), t ∈ [0; T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t; u(t)), u(0) = 0.
Publié le : 2000-07-05
Classification:  Heat-kernel estimates,  Maximal L^p-L^q-regularity,  Non-autonomous Cauchy problem,  Singular integrals,  35B45, 35Kxx, 47B20, 47D06,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 
@article{hal-00535645,
     author = {Hieber, Matthias and Monniaux, Sylvie},
     title = {Heat-kernels and maximal Lp - Lq-estimates: the non-autonomous case},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00535645}
}

Hieber, Matthias; Monniaux, Sylvie. Heat-kernels and maximal Lp − Lq−estimates: the non-autonomous case. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00535645/