We give two results about Harnack type inequalities.First,on Riemannian surfaces,we have an estimate of type sup+inf.The second result concern the solutions of prescribed scalar curvature equation on the unit ball of ...We give two results about Harnack type inequalities.First,on Riemannian surfaces,we have an estimate of type sup+inf.The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition.Next,we give an inequality of type(supK^u)^2s-1×infπu≤c for positive solutions of△u=V u^5 onΩbelong toR^3,where K is a compact set ofΩand V is s-Holderian,s∈]-1/2,1].For the case s=1/2 andΩ=S3,we prove that,if minΩu〉m〉0(for some particular constant m〉0),and the H¨olderian constant A of V tends to 0(in certain meaning),we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set ofΩ.展开更多
We consider the following problem on bounded open setΩof R^(n)■We assume that:■Then,we have a sup×inf inequality for the solutions of the previous equation,namely:■.
文摘We give two results about Harnack type inequalities.First,on Riemannian surfaces,we have an estimate of type sup+inf.The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition.Next,we give an inequality of type(supK^u)^2s-1×infπu≤c for positive solutions of△u=V u^5 onΩbelong toR^3,where K is a compact set ofΩand V is s-Holderian,s∈]-1/2,1].For the case s=1/2 andΩ=S3,we prove that,if minΩu〉m〉0(for some particular constant m〉0),and the H¨olderian constant A of V tends to 0(in certain meaning),we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set ofΩ.
文摘We consider the following problem on bounded open setΩof R^(n)■We assume that:■Then,we have a sup×inf inequality for the solutions of the previous equation,namely:■.
