The Meyers Estimates for Domains Perforated along the Boundary

Article Mathematics

Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

Dumitru Motreanu et al.

Summary: The paper introduces a sub-supersolution approach for quasilinear elliptic equations with a degenerated p-Laplacian and a convection term. It establishes the existence and location of solutions through this approach and applies it to find nontrivial, nonnegative and bounded solutions. The presence of the degenerated operator requires a substantial change to the functional setting of previous works.

MATHEMATICS (2021)

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Article Mathematics, Applied

Elliptic Problems with Additional Unknowns in Boundary Conditions and Generalized Sobolev Spaces

Anna Anop et al.

Summary: This article focuses on elliptic differential problems in generalized inner product Sobolev spaces, with additional unknown functions or distributions in the boundary conditions. By parametrizing these spaces, the regularity of distributions is more finely characterized, inducing Fredholm bounded operators on appropriate pairs of spaces. New sufficient conditions are found for components of solutions to have continuous classical derivatives of given orders.

AXIOMS (2021)

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Article Mechanics

The Meyer's estimate of solutions to Zaremba problem for second-order elliptic equations in divergent form

Yurij A. Alkhutov et al.

Summary: This paper provides an estimate for the increased integrability of the gradient of the solution to the Zaremba problem for a divergent elliptic operator in a bounded domain with nontrivial capacity of the Dirichlet boundary conditions.

COMPTES RENDUS MECANIQUE (2021)

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Article Mathematics