1,721,025 research outputs found
A paper of Legendre revisited
No full textIn [4] Legendre discusses the set of admissible functions for Newton's variational
problem of minimal resistance. He proposes a particular side constraint to ensure existence of
a solution. Here we give a rigorous proof of his result and discuss some related problems
The p-Laplace eigenvalue problem as p goes to 1 and Cheeger sets in a Finsler metric
No full textWe consider the p-Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit problem as p -> 1
On Newton's problem under side constraints
No full textWe give a survey of some results on Newton's problem of minimal resistance obtained in [1] and we present a new result for the class of fixed surface
A direct uniqueness proof for equations involving the -Laplace operator
No full textWe provide a simple convexity argument for some known uniqueness theorems.
Previous proofs were more technical and had to pay attention to the behaviour of
solutions near the boundary
A Symmetry Problem Related to Wirtinger's and Poincaré's Inequality
No full textWe study the minimizers of J(u), the p-norm of u' divided by the q-norm of u, among periodic functions with mean value 0. Here p,q are integers bigger than 1. We extend a result obtained by Dacorogna, Gangbo and Subia
The p--laplace eigenvalue problem and viscosity solutions as in a Finsler metric.
No full textWe consider the p-Laplacian operator on a domain equipped with a Finsler metric. We
recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as
p go to infinity
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