On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness

2017/05/25 by Mikulevicius, R., Phonsom, C. · 4 citations
#35B65 #35R09 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.09256

Abstract

Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some rough probability density function estimates of the associated Levy process are used as well.

Cited by

• The time fractional stochastic partial differential equations with non-local operator on ℝ^d
• A note on the L^p-solvability of a strongly-coupled nonlocal system of equations
• Local/global well-posedness analysis of time-space fractional Schrödinger equation on ℝ^d
• Muckenhoupt-weighted L_q(L_p) boundedness for time-space fractional nonlocal operators

Related

• On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness
• On Lp -theory for parabolic and elliptic integro-differential equations with scalable operators in the whole space
• On the Cauchy problem for stochastic integro-differential equations with radially O-regularly varying Levy measure
• On the Cauchy problem for nondegenerate parabolic integro-differential equations in the scale of generalized Hölder spaces
• On the Cauchy problem for parabolic integro-differential equations in generalized Hölder spaces