This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates.
Motreanu D., Tornatore E. (2024). DIRICHLET PROBLEMS WITH ANISOTROPIC PRINCIPAL PART INVOLVING UNBOUNDED COEFFICIENTS. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2024(1-??), 1-13 [10.58997/ejde.2024.11].
DIRICHLET PROBLEMS WITH ANISOTROPIC PRINCIPAL PART INVOLVING UNBOUNDED COEFFICIENTS
Tornatore E.Secondo
2024-01-30
Abstract
This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates.
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