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<p>In this paper, a large deviation principle for the strong solution of the <i>p</i> Laplace equation on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment estimate play a crucial role in establishing the large deviation principle. Moreover, based on the Girsanov transformation and the standard approach of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-uniqueness, the quadratic transportation cost information inequality is proved for a strong solution to the underlying problem— which then implies the measure concentration phenomenon.</p>

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Nonlinear Stochastic Laplace Equation: Large Deviation and Measure Concentration

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Ananta K. Majee

摘要

In this paper, a large deviation principle for the strong solution of the p Laplace equation on \(\mathbb {R}^d\) R d driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment estimate play a crucial role in establishing the large deviation principle. Moreover, based on the Girsanov transformation and the standard approach of \(L^2\) L 2 -uniqueness, the quadratic transportation cost information inequality is proved for a strong solution to the underlying problem— which then implies the measure concentration phenomenon.