We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $Delta_lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin type operators $$ Delta_{x}+ |x|^{2alpha}Delta_{y},qquad (x,y)inmathbb{R}^{N_1} imesmathbb{R}^{N_2}, alphageq 0, $$ which were proved to be sharp.
Hardy type inequalities for Δλ-Laplacians
KOGOJ, ALESSIA ELISABETTA;
2016
Abstract
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $Delta_lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin type operators $$ Delta_{x}+ |x|^{2alpha}Delta_{y},qquad (x,y)inmathbb{R}^{N_1} imesmathbb{R}^{N_2}, alphageq 0, $$ which were proved to be sharp.File in questo prodotto:
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