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

none4sìIn 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 $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain, $N\ge1$, $\lambda>0$, $0<q<\frac{N+\alpha}{N-\alpha}$, $0<\alpha<\min\{N,2\}$. For suitable conditions on $\alpha$ depending on $q$, we prove: In the case $q<1$, there exist at least two solutions for every $0<\lambda<\Lambda$ and some $\Lambda>0$, at least one if $\lambda=\Lambda$, no solution if $\lambda>\Lambda$. For $q=1$ we show existence of at least one solution for $01$ the existence is shown for every $\lambda>0$. 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