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
Keyword(s):  
Riemannian Manifold ◽  
Elliptic Equation ◽  
Compact Riemannian Manifold ◽  
Critical Growth ◽  
Linear Elliptic Equation

scholarly journals Second-Order Elliptic Equation with Singularities

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Hichem Boughazi
Keyword(s):  
Riemannian Manifold ◽  
Elliptic Equation ◽  
Compact Riemannian Manifold ◽  
Second Order ◽  
Singular Equation ◽  
Order Elliptic Equation ◽  
Nontrivial Solutions ◽  
Geometric Application ◽  
Second Order Elliptic Equation

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.

A gradient estimate on a manifold with convex boundary

1997 ◽  
Vol 127 (1) ◽  
pp. 171-179 ◽  
Author(s):  
Zhongmin Qian
Keyword(s):  
Parabolic Equation ◽  
Riemannian Manifold ◽  
Elliptic Equation ◽  
Nonlinear Parabolic Equation ◽  
Compact Riemannian Manifold ◽  
Gradient Estimate ◽  
Markov Semigroup ◽  
Complete Manifold ◽  
Convex Boundary ◽  
Nonlinear Parabolic

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.

Nonhomogeneous polyharmonic elliptic problems involving GJMS operator on Riemannian manifold

2019 ◽  
Vol 13 (06) ◽  
pp. 2050115 ◽  
Author(s):  
Kamel Tahri
Keyword(s):  
Riemannian Manifold ◽  
Elliptic Equation ◽  
Scalar Curvature ◽  
Elliptic Equations ◽  
Critical Sobolev Exponent ◽  
Henri Poincaré ◽  
Linear Elliptic Equation ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Sobolev Exponent

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.

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

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.

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

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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