Elliptic Harnack inequalities for mixed local and nonlocal $p$-energy form on metric measure spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866912943863496704 |
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| author | Chen, Aobo Yu, Zhenyu |
| author_facet | Chen, Aobo Yu, Zhenyu |
| contents | In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal $p$-energy forms. Within this framework, we use the Poincaré inequality, the cutoff Sobolev inequality, and mild assumptions on the jump measure to establish the weak and strong elliptic Harnack inequalities for such mixed forms. Our approach is based on the De Giorgi--Nash--Moser method and extends the corresponding results for Dirichlet forms without the killing part, as well as for mixed energy forms on Euclidean spaces. Some consequences of elliptic Harnack inequalities are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic Harnack inequalities for mixed local and nonlocal $p$-energy form on metric measure spaces Chen, Aobo Yu, Zhenyu Analysis of PDEs Functional Analysis Primary 35B45, 35D99, secondary 35R11, 31C45, 31E05, 39B62, 46E36 In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal $p$-energy forms. Within this framework, we use the Poincaré inequality, the cutoff Sobolev inequality, and mild assumptions on the jump measure to establish the weak and strong elliptic Harnack inequalities for such mixed forms. Our approach is based on the De Giorgi--Nash--Moser method and extends the corresponding results for Dirichlet forms without the killing part, as well as for mixed energy forms on Euclidean spaces. Some consequences of elliptic Harnack inequalities are discussed. |
| title | Elliptic Harnack inequalities for mixed local and nonlocal $p$-energy form on metric measure spaces |
| topic | Analysis of PDEs Functional Analysis Primary 35B45, 35D99, secondary 35R11, 31C45, 31E05, 39B62, 46E36 |
| url | https://arxiv.org/abs/2510.12404 |