ترغب بنشر مسار تعليمي؟ اضغط هنا

Hardy inequalities for p-Laplacians with Robin boundary conditions

321   0   0.0 ( 0 )
 نشر من قبل Hynek Kovarik
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

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.
For a bounded convex domain Omega in R^N we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of Omega, the volume of $Omega$, as well as a finite number of sharp logarithmic corrections. We also discuss the best constant of these inequalities.
189 - A.E. Kogoj , S. Sonner 2014
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.
We present a unified approach to improved $L^p$ Hardy inequalities in $R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is taken from a s urface of codimension $1<k<N$. In our main result we add to the right hand side of the classical Hardy inequality, a weighted $L^p$ norm with optimal weight and best constant. We also prove non-homogeneous improved Hardy inequalities, where the right hand side involves weighted L^q norms, q eq p.
For Schrodinger operators on an interval with either convex or symmetric single-well potentials, and Robin or Neumann boundary conditions, the gap between the two lowest eigenvalues is minimised when the potential is constant. We also have results for the $p$-Laplacian.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا