961 research outputs found
Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data
In this work we study regularity properties of solutions to fractional
elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with
the Spectral Fractional Laplacian
A critical fractional equation with concave-convex power nonlinearities
none4sĂŹIn this work we study a fractional critical problem with concave-convex nonlinearities. Our main results show the existence and multiplicity of solutions to this problem for different values of the real parameter appearing in the equation. The dependency on this parameter changes according to whether we consider the concave power case or the convex power case. These two cases will be treated separatelyopenBarrios B; Colorado E; Servadei R; Soria FBarrios, B; Colorado, E; Servadei, Raffaella; Soria, F
Colorado River Basin Study Comments--Bureau of Land Managment, Colorado Office
Comments on the Colorado River Basin Study prepared by the the Western Water Policy Review Advisory Commission
On some Critical Problems for the Fractional Laplacian Operator
We study the effect of lower order perturbations in the existence of positive
solutions to the following critical elliptic problem involving the fractional
Laplacian: (-\Delta)^{\alpha/2}u=\lambda u^q+u^{\frac{N+\alpha}{N-\alpha}},
\quad u>0 &\quad in \Omega, u=0&\quad on \partial\Omega, where
is a smooth bounded domain, , ,
, . For suitable
conditions on depending on , we prove: In the case , there
exist at least two solutions for every and some
, at least one if , no solution if
. For we show existence of at least one solution for
the existence is shown for every . Also we prove that the solutions
are bounded and regular
People as Part of Ecosystems
30 p. : ill. ; 28 cmhttps://scholar.law.colorado.edu/books_reports_studies/1049/thumbnail.jp
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