Conical stochastic maximal $L^p$-regularity for $1 \leq p \lt \infty$
Conical stochastic maximal $L^p$-regularity for $1 \leq p \lt \infty$
Let $A = -{\rm div} \,a(\cdot) \nabla$ be a second order divergence form elliptic operator on $\R^n$ with bounded measurable real-valued coefficients and let $W$ be a cylindrical Brownian motion in a Hilbert space $H$. Our main result implies that the stochastic convolution process $$ u(t) = \int_0^t e^{-(t-s)A}g(s)\,dW(s), \quad t\ge 0,$$ satisfies, for all $1\le p
minor corrections. Final before publication in Math. Annalen
- Australian National University Australia
- Laboratoire Paul Painlevé France
- Australian Mathematical Sciences Institute Australia
- Far East Branch of the Russian Academy of Sciences Russian Federation
- Department of Mathematical Sciences Russian Federation
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], stochastic convolutions, Probability (math.PR), [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], off-diagonal estimates, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Functional Analysis (math.FA), tent spaces, Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Conical maximal $L^p$-regularity, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Probability, Analysis of PDEs (math.AP)
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], stochastic convolutions, Probability (math.PR), [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], off-diagonal estimates, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Functional Analysis (math.FA), tent spaces, Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Conical maximal $L^p$-regularity, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Probability, Analysis of PDEs (math.AP)
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