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Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data
semigroup Riemannian manifolds singular data
2010/11/12
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initial condition. We sho...
Biharmonic Equation and an Improved Hardy Inequality
Biharmonic equation Hardy inequality nontrivial solution
2007/12/12
An improved Hardy inequality will be proven in thepresent work. Using the improved Hardy inequality and variationaltechniques, we also discuss the existence of nontrivial solutionfor following the we...