We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account is very general and comprises also the singular and degenerate nonlinear case with non-standard growth conditions. The sourcing term is also allowed to have a very general form, depending on the space variables, on the solution itself, on its gradient, and possibly on higher order derivatives if additional structural conditions are satisfied.

Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities / C. Cavaterra, S. Dipierro, A. Farina, Z. Gao, E. Valdinoci. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 270(2020), pp. 435-475. [Epub ahead of print] [10.1016/j.jde.2020.08.007]

Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities

C. Cavaterra;
2020

Abstract

We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account is very general and comprises also the singular and degenerate nonlinear case with non-standard growth conditions. The sourcing term is also allowed to have a very general form, depending on the space variables, on the solution itself, on its gradient, and possibly on higher order derivatives if additional structural conditions are satisfied.
Regularity theory; Singular and degenerate equations; (p, q)-Laplacian; Pointwise gradient estimates in terms of a potential function
Settore MAT/05 - Analisi Matematica
JOURNAL OF DIFFERENTIAL EQUATIONS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/769301
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