Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908940239896576 |
|---|---|
| author | Baadi, Khalid |
| author_facet | Baadi, Khalid |
| contents | In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$-weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser's $L^2$-$L^\infty$ estimates for local weak solutions. In the special case of real coefficients, Moser's $L^2$-$L^\infty$ estimates are known, which provide an easier proof of Gaussian upper bounds, and a known Harnack inequality is then used to derive Gaussian lower bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds Baadi, Khalid Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 35A08, 35K65, 35K15 Secondary: 35K08, 35K10 In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$-weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser's $L^2$-$L^\infty$ estimates for local weak solutions. In the special case of real coefficients, Moser's $L^2$-$L^\infty$ estimates are known, which provide an easier proof of Gaussian upper bounds, and a known Harnack inequality is then used to derive Gaussian lower bounds. |
| title | Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 35A08, 35K65, 35K15 Secondary: 35K08, 35K10 |
| url | https://arxiv.org/abs/2503.07569 |