English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A metric measure space equipped with a Dirichlet form is called recurrent ifits Hausdorff dimension is less than its walk dimension. In bounded domains ofsuch spaces we study the parabolic Anderson models \[ \partial_{t} u(t,x) =\Delta u(t,x) + \beta u(t,x) \, \dot{W}_\alpha(t,x) \] where the noise$W_\alpha$ is white in time and colored in space when $\alpha >0$ while for$\alpha=0$ it is also white in space. Both Dirichlet and Neumann boundaryconditions are considered. Besides proving existence and uniqueness in theIt\^o sense we also get precise $L^p$ estimates for the moments andintermittency properties of the solution as a consequence. Our study revealsnew exponents which are intrinsically associated to the geometry of theunderlying space and the results for instance apply in metric graphs orfractals like the Sierpi\'nski gasket for which we prove scaling invarianceproperties of the models.

Parabolic Anderson model in bounded domains of recurrent metric measure spaces