We prove a priori estimates for solutions of the Poisson and heat equations in weighted spaces of Kondrat'ev type. The weight is a power of the distance from a distinguished axis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-6, author = {Adam Kubica and Wojciech M. Zaj\k aczkowski}, title = {A priori estimates in weighted spaces for solutions of the Poisson and heat equations}, journal = {Applicationes Mathematicae}, volume = {34}, year = {2007}, pages = {431-444}, zbl = {1135.35324}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-6} }
Adam Kubica; Wojciech M. Zajączkowski. A priori estimates in weighted spaces for solutions of the Poisson and heat equations. Applicationes Mathematicae, Tome 34 (2007) pp. 431-444. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-6/