We prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form A E(x)∇u + div(u E(x)), with A > 0 and E in (Lr (Ω))N . The result is obtained using a nonlinear function of u as test function, in order to “cancel” this term.
Dirichlet problems with skew-symmetric drift terms / Boccardo, L.; Casado-Diaz, J.; Orsina, L.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 362:(2024), pp. 301-306. [10.5802/crmath.564]
Dirichlet problems with skew-symmetric drift terms
Boccardo L.;Orsina L.
2024
Abstract
We prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form A E(x)∇u + div(u E(x)), with A > 0 and E in (Lr (Ω))N . The result is obtained using a nonlinear function of u as test function, in order to “cancel” this term.File allegati a questo prodotto
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