اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHardy Type Inequalities for $Delta_lambda$-Laplacians
195
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 $$ Delta_{x}+ |x|^{2alpha}Delta_{y},qquad (x,y)inmathbb{R}^{N_1}timesmathbb{R}^{N_2}, alphageq 0, $$ which were proved to be sharp.
قيم البحث
اقرأ أيضاً
In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals $((p-1)/p)^p$ whenever Dirichlet boundary conditions are
imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.
The sharp trace inequality of Jose Escobar is extended to traces for the fractional Laplacian on R^n and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Liebs sharp form of the Hardy-Littlewood-Sobolev inequality.
We consider a general class of sharp $L^p$ Hardy inequalities in $R^N$ involving distance from a surface of general codimension $1leq kleq N$. We show that we can succesively improve them by adding to the right hand side a lower order term with optim
al weight and best constant. This leads to an infinite series improvement of $L^p$ Hardy inequalities.
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A striking o
pen question is the possibility of concentration which is analyzed and related with nonlinear diffusion equations involving mean field drifts.
In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in mis
cellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
