Máté Gerencsér

On the solvability of degenerate stochastic partial differential equations in Sobolev spaces

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric hyperbolic systems.

On the boundedness of solutions of SPDEs

In this paper estimates for the

Singular SPDEs in domains with boundaries

L_\infty

Local L∞-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs

L∞-norm of solutions of parabolic SPDEs are derived. The result is obtained through iteration techniques, motivated by the work of Moser in deterministic settings. As an application of the main result, solvability of a class of semilinear SPDEs is established.

Localization errors in solving stochastic partial differential equations in the whole space

We discuss

Entropy solutions for stochastic porous media equations

L_p