Calderón–Zygmund theory for nonlinear elliptic problems with irregular obstacles

By Sun-Sig Byun, Yumi Cho, Lihe Wang. 2012

59 citations recorded by the source corpus.

Abstract We consider a nonhomogeneous elliptic problem with an irregular obstacle involving a discontinuous nonlinearity over an irregular domain in divergence form of p-Laplacian type, to establish the global Calderon–Zygmund estimate by proving that the gradient of the weak solution is as integrable as both the gradient of the obstacle and the nonhomogeneous term under the BMO smallness of the nonlinearity and sufficient flatness of the boundary in the Reifenberg sense.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e0c8ca4456c748b32141f7c3233771d045b2935

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Non-autonomous functionals, borderline cases and related function classes (2016, unknown): “7] and [10].”
Higher differentiability for solutions to a class of obstacle problems (2018, methodology): “Obstacle problems with V M O coefficients are known to have a nice L p theory (see [9]) and we take advantage from this result through the embedding Theorems in Besov spaces ([28] and Sect.”
Lorentz estimates for degenerate and singular evolutionary systems (2013, unknown): “1”
Bounded Minimisers of Double Phase Variational Integrals (2015, result): “Similar results are also contained in [9], actually under more general assumptions both on the equations considered and on the domain Ω.”