scholarly journals The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition

2021 ◽  
Vol 3 (4) ◽  
pp. 1-20
Author(s):  
François Murat ◽  
◽  
Alessio Porretta ◽  
◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Ergodic Limit

Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moloud Makvand Chaharlang ◽  
Abdolrahman Razani
Keyword(s):  
Boundary Condition ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Neumann Boundary Condition ◽  
Mountain Pass Theorem ◽  
Minimum Principle ◽  
Neumann Boundary ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

AbstractIn this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces.

A functional-analytic framework for the study of elliptic equations on variable domains

1990 ◽  
Vol 116 (3-4) ◽  
pp. 367-380 ◽  
Author(s):  
José M. Vegas
Keyword(s):  
Boundary Condition ◽  
Hilbert Space ◽  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Analytic Framework ◽  
Orthogonal Projections ◽  
Variable Domains

SynopsisGiven a decreasing sequence of domains Ωn converging in measure to some domain Ω0, a sequence of subspaces V of a Hilbert space V is constructed in such a way that the convergence of the solutions of u −Δu = f on Ωn with Neumann Boundary Condition is given in terms of the convergence of the orthogonal projections Pn on Vn. Under dissipative assumptions, we can obtain continuation results for equations like u −Δu = f(x,u ∇u).

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