Browsing by Author "Otto, Felix"
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- ItemMoment bounds for the corrector in stochastic homogenization of a percolation model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Lamacz, Agnes; Neukamm, Stefan; Otto, FelixWe study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on Zd, d > 2. The model is obtained from the classical {0,1}-Bernoulli bond percolation by conditioning all bonds parallel to the first coordinate direction to be open. As a main result we prove (in fact for a slightly more general model) that stationary correctors exist and that all finite moments of the corrector are bounded. This extends a previous result in [8], where uniformly elliptic conductances are treated, to the degenerate case. Our argument is based on estimates on the gradient of the elliptic Green's function.
- ItemPartielle Differentialgleichungen(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2003) Otto, Felix; Simon, Leon[no abstract available]
- ItemPhase Transitions(Zürich : EMS Publ. House, 2010) Ioffe, Dmitri; Luckhaus, Stephan; Otto, FelixPhase transitions are common phenomena which occur in many fields of material sciences. Models of phase transitions in diverse physical systems often lead to ill-posed mathematical problems whose solutions are characterized by oscillations, bifurcations and singularities. Random fluctuations and stochastic events also play an important role in determining the nature of the solutions.
- ItemQuantification of ergodicity in stochastic homogenization: Optimal bounds via spectral gap on Glauber dynamics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Gloria, Antoine; Neukamm, Stefan; Otto, FelixWe study quantitatively the effective large-scale behavior of discrete elliptic equations on the lattice Zd with random coefficients. The theory of stochastic homogenization relates the random, stationary, and ergodic field of coefficients with a deterministic matrix of effective coefficients. This is done via the corrector problem, which can be viewed as a highly degenerate elliptic equation on the infinite-dimensional space of admissible coefficient fields. In this contribution we develop new quantitative methods for the corrector problem based on the assumption that ergodicity holds in the quantitative form of a Spectral Gap Estimate w. r. t. a Glauber dynamics on coefficient fields |as it is the case for independent and identically distributed coefficients. As a main result we prove an optimal decay in time of the semigroup associated with the corrector problem (i. e. of the generator of the process called "random environment as seen from the particle").
- ItemVariational Methods for Evolution(Zürich : EMS Publ. House, 2011) Otto, Felix; Savare, Giuseppe; Stefanelli, UlisseThe meeting focused on the last advances in the applications of variational methods to evolution problems governed by partial differential equations. The talks covered a broad range of topics, including large deviation and variational principles, rate-independent evolutions and gradient flows, heat flows in metric-measure spaces, propagation of fracture, applications of optimal transport and entropy-entropy dissipation methods, phase-transitions, viscous approximation, and singular-perturbation problems.