scholarly journals A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary

2010 ◽  
Vol 38 (3) ◽  
pp. 317-334 ◽  
Author(s):  
João Marcos do Ó ◽  
Yunyan Yang
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Hichem Boughazi

On the compact Riemannian manifold of dimension n≥5, we study the existence and regularity of nontrivial solutions for nonlinear second-order elliptic equation with singularities. At the end, we give a geometric application of the above singular equation.


Author(s):  
Zhongmin Qian

We present a simple probability approach for establishing a gradient estimate for a solution of an elliptic equation on a compact Riemannian manifold with convex boundary, or on a noncompact complete manifold. Our method can also be applied to derive a similar gradient estimate for a nonlinear parabolic equation, and an abstract gradient estimate for a Markov semigroup.


2019 ◽  
Vol 13 (06) ◽  
pp. 2050115 ◽  
Author(s):  
Kamel Tahri

Let [Formula: see text] be a closed Riemannian manifold, under some assumptions on [Formula: see text] and [Formula: see text] by applying a method used in [Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Ann. Inst. Henri Poincaré 9 (1992) 281–304], we show the existence and multiplicity of solutions of the semi-linear elliptic equation: [Formula: see text]. When [Formula: see text] is an Einsteinian manifold of positive scalar curvature, under additional conditions, we obtain the existence of positive solutions.


1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.


Author(s):  
David E. Blair

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.


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