On Lp-solutions of semilinear stochastic partial differential equations

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Degenerate parabolic stochastic partial differential equations (2013, unknown): “Nevertheless, kinetic formulation can be derived only for smooth solutions hence the classical result [13] giving L-valued solutions for the nondegenerate case has to be improved (see [15]).”
Lp estimates for the uniform norm of solutions of quasilinear SPDE's (2005, unknown): “We should also mention that Gy¨ ongy and Rovira [ 9 ] derived L p -estimates by deriving first L p -estimates for the Green kernel.”
Scalar conservation laws with stochastic forcing (2010, methodology): “It is shown in [ GR00 ] that equation (37) has a unique Lρ(TN) valued continuous solution provided ρ is large enough and u0 ∈ Lρ(TN), hence in particular for u0 ∈ L∞(TN).”
Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise (2019, background): “Several papers in the literature discuss stochastic PDEs with locally Lipschitz coefficients that have polynomial growth and/or satisfy certain monotonicity conditions (see [4, 11, 18, 21, 22], for instance).”