The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem , . The continuity of u with respect to both h and t has been considered in [6].
@article{bwmeta1.element.bwnjournal-article-apmv56z3p311bwm, author = {T. Winiarska}, title = {Regularity of solutions of parabolic equations with coefficients depending on t and parameters}, journal = {Annales Polonici Mathematici}, volume = {57}, year = {1992}, pages = {311-317}, zbl = {0763.35015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv56z3p311bwm} }
T. Winiarska. Regularity of solutions of parabolic equations with coefficients depending on t and parameters. Annales Polonici Mathematici, Tome 57 (1992) pp. 311-317. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z3p311bwm/
[000] [1] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, 1981. | Zbl 0456.35001
[001] [2] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. | Zbl 0148.12601
[002] [3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
[003] [4] P. E. Sobolevskiĭ, On equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obshch. 10 (1986), 297-350 (in Russian).
[004] [5] H. Tanabe, Equations of Evolution, Pitman, 1979.
[005] [6] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. | Zbl 0738.35020
[006] [7] T. Winiarska, Evolution equation with parameter, Univ. Iag. Acta Math. 28 (1987), 219-227. | Zbl 0673.47035
[007] [8] T. Winiarska, Differential Equations with Parameters, Monograph 68, Technical University of Cracow, 1988.
[008] [9] K. Yosida, Functional Analysis, Springer, 1980.