# Ergodicity and Local Limits for Stochastic Local and Nonlocal p-Laplace Equations

@article{Gess2016ErgodicityAL,
title={Ergodicity and Local Limits for Stochastic Local and Nonlocal p-Laplace Equations},
author={Benjamin Gess and Jonas M. T{\"o}lle},
journal={SIAM J. Math. Anal.},
year={2016},
volume={48},
pages={4094-4125}
}
• Published 2016
• Computer Science, Mathematics
• SIAM J. Math. Anal.
• Ergodicity for local and nonlocal stochastic singular $p$-Laplace equations is proven, without restriction on the spatial dimension and for all $p\in[1,2)$. This generalizes previous results from [B. Gess and J. M. Tolle, J. Math. Pures Appl., 101 (2014), pp. 789--827], [W. Liu and J. M. Tolle, Electron. Commun. Probab., 16 (2011), pp. 447--457], [W. Liu, J. Evol. Equations, 9 (2009), pp. 747--770]. In particular, the results include the multivalued case of the stochastic (nonlocal) total… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 80 REFERENCES

## Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem

• Mathematics
• 1981

## A nonlocal p-Laplacian evolution equation with Neumann boundary conditions

• Mathematics
• 2008
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## Nonlocal diffusion problems

VIEW 3 EXCERPTS

## Exponential Convergence of Non-Linear Monotone SPDEs

VIEW 3 EXCERPTS

## A Nonlocal p-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions

• Computer Science, Mathematics
• SIAM J. Math. Anal.
• 2008
VIEW 2 EXCERPTS

## Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

• Mathematics, Physics
• 2008
VIEW 1 EXCERPT

## Decay estimates for a nonlocal $p-$Laplacian evolution problemwith mixed boundary conditions

• Mathematics
• 2014

## Decay estimates for nonlocal problems via energy methods

• Mathematics
• 2009

## Convergence of invariant measures for singular stochastic diffusion equations

• Mathematics
• 2012
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## On ergodicity of some Markov processes

• Mathematics
• 2010
VIEW 2 EXCERPTS