scholarly journals A singular elliptic problem involving fractional p-Laplacian and a discontinuous critical nonlinearity

2021 ◽  
Vol 62 (7) ◽  
pp. 071505
Author(s):  
Kamel Saoudi ◽  
Akasmika Panda ◽  
Debajyoti Choudhuri
Keyword(s):  
Elliptic Problem ◽  
Critical Nonlinearity

scholarly journals On an Elliptic Problem with Critical Nonlinearity in Expanding Annuli

1999 ◽  
Vol 163 (1) ◽  
pp. 29-62 ◽  
Author(s):  
Mohameden O. Ahmedou ◽  
Khalil O. El Mehdi
Keyword(s):  
Elliptic Problem ◽  
Critical Nonlinearity

scholarly journals Non-degeneracy of least-energy solutions for an elliptic problem with nearly critical nonlinearity

2010 ◽  
Vol 140 (1) ◽  
pp. 203-222
Author(s):  
Futoshi Takahashi
Keyword(s):  
Recent Result ◽  
Bounded Domain ◽  
Elliptic Problem ◽  
Positive Function ◽  
Coefficient Function ◽  
Critical Nonlinearity ◽  
Smooth Bounded Domain ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Smooth Positive Function

We consider the problem −Δu = c0K(x)upε, u > 0 in Ω, u = 0 on δΩ, where Ω is a smooth, bounded domain in ℝN, N ≥ 3, c0 = N(N − 2), pε = (N + 2)/(N − 2) − ε and K is a smooth, positive function on . We prove that least-energy solutions of the above problem are non-degenerate for small ε > 0 under some assumptions on the coefficient function K. This is a generalization of the recent result by Grossi for K ≡ 1, and needs precise estimates and a new argument.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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