An L p -estimate for the stochastic heat equation on an angular domain in R 2

Petru A. Cioica-Licht, Kyeong Hun Kim, Kijung Lee, Felix Lindner

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove a weighted L p -estimate for the stochastic convolution associated with the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain Dκ0⊂R2 with angle κ∈ (0 , 2 π). Furthermore, we use this estimate to establish existence and uniqueness of a solution to the corresponding equation in suitable weighted L p -Sobolev spaces. In order to capture the singular behaviour of the solution and its derivatives at the vertex, we use powers of the distance to the vertex as weight functions. The admissible range of weight parameters depends explicitly on the angle κ.

Original languageEnglish
Pages (from-to)45-72
Number of pages28
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume6
Issue number1
DOIs
Publication statusPublished - 2018 Mar 1

Fingerprint

Stochastic Heat Equation
Sobolev spaces
Convolution
Boundary conditions
Derivatives
Angle
Vertex of a graph
Weight Function
Estimate
Sobolev Spaces
Dirichlet Boundary Conditions
Existence and Uniqueness
Derivative
Zero
Range of data
Hot Temperature

Keywords

  • Angular domain
  • Corner singularity
  • Non-smooth domain
  • Stochastic heat equation
  • Stochastic partial differential equation
  • Weighted L -estimate
  • Weighted Sobolev regularity

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

An L p -estimate for the stochastic heat equation on an angular domain in R 2 . / Cioica-Licht, Petru A.; Kim, Kyeong Hun; Lee, Kijung; Lindner, Felix.

In: Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 6, No. 1, 01.03.2018, p. 45-72.

Research output: Contribution to journalArticle

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