Nonlinear stochastic Laplace equation: Large Deviations and Measure Concentration
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914924957007872 |
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| author | Majee, Ananta K |
| author_facet | Majee, Ananta K |
| contents | In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment estimate plays a crucial role to establish the large deviation principle. Moreover, based on the Girsanov transformation and the standard L2-uniqueness approach, the quadratic transportation cost information inequality is proved for the strong solution to the underlying problem which then implies the measure concentration phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14742 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear stochastic Laplace equation: Large Deviations and Measure Concentration Majee, Ananta K Probability Analysis of PDEs In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment estimate plays a crucial role to establish the large deviation principle. Moreover, based on the Girsanov transformation and the standard L2-uniqueness approach, the quadratic transportation cost information inequality is proved for the strong solution to the underlying problem which then implies the measure concentration phenomenon. |
| title | Nonlinear stochastic Laplace equation: Large Deviations and Measure Concentration |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2408.14742 |