ترغب بنشر مسار تعليمي؟ اضغط هنا

Bismut hypoelliptic Laplacians for manifolds with boundaries

66   0   0.0 ( 0 )
 نشر من قبل Francis Nier
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Francis Nier




اسأل ChatGPT حول البحث

Boundary conditions for Bismuts hypoelliptic Laplacian which naturally correspond to Dirichlet and Neumann boundary conditions for Hodge Laplacians are considered. Those are related with specific boundary conditions for the differential and its various adjoints. Once the closed realizations of those operators are well understood, the commutation of the differential with the resolvent of the hypoelliptic Laplacian is checked with other properties like the PT-symmetry, which are important for the spectral analysis.



قيم البحث

اقرأ أيضاً

115 - Qingsong Wang , Bo Yang , 2016
In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi -invariant metric and a compatible left invariant complex structure. In particular, isosceles Hopf surfaces are the only Bismut flat compact non-Kahler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds.
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.
294 - Amit Einav , Michael Loss 2011
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.
199 - 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 consider nonnegative solutions $u:Omegalongrightarrow mathbb{R}$ of second order hypoelliptic equations begin{equation*} mathscr{L} u(x) =sum_{i,j=1}^n partial_{x_i} left(a_{ij}(x)partial_{x_j} u(x) right) + sum_{i=1}^n b_i(x) partial_{x_i} u(x) = 0, end{equation*} where $Omega$ is a bounded open subset of $mathbb{R}^{n}$ and $x$ denotes the point of $Omega$. For any fixed $x_0 in Omega$, we prove a Harnack inequality of this type $$sup_K u le C_K u(x_0)qquad forall u mbox{ s.t. } mathscr{L} u=0, ugeq 0,$$ where $K$ is any compact subset of the interior of the $mathscr{L}$-propagation set of $x_0$ and the constant $C_K$ does not depend on $u$.
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