Work

Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds

Year: 2026

Type: article

Abstract: 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 $$A_2$$ A 2 -weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser’s $$L^2$$ L 2 - $$L^\infty $$ L ∞ estimates for local weak solutions. In the special case of real coefficients, Moser’s $$L^2$$ L 2 - $$L^\infty $$ L ∞ 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.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-026-01201-1

Author: Khalid Baadi

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Université Paris-Saclay