Gradient estimates in Orlicz space for nonlinear elliptic equations

By Sun-Sig Byun, Fengping Yao, Shulin Zhou. 2008

78 citations recorded by the source corpus.

Abstract In this paper we generalize gradient estimates in L p space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b79f4d65db6c39a285c0dd8fd60099329188beaa

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In Applied Mathematics

1. N. Phuc
2. Sun-Sig Byun
3. Lihe Wang
4. Seungjin Ryu
5. Tadele Mengesha
6. Giuseppe Mingione
7. Jihoon Ok
8. Doyoon Kim

In Computational Theory and Mathematics

1. N. Phuc
2. Sun-Sig Byun
3. Lihe Wang
4. Seungjin Ryu
5. Tadele Mengesha
6. Jihoon Ok
7. Giuseppe Mingione
8. Doyoon Kim

Citations in the corpus

• New Orlicz–Hardy spaces associated with divergence form elliptic operators (2009, unknown): “oped and the spaces have been widely used in probability, statistics, potential theory, partial differential equations, as well as harmonic analysis and some other fields of analysis; see, for example, [34, 35, 9, 31, 1, 26]. Moreover, the Orlicz-Hardy spaces are also good substitutes of the Orlicz sp”
• Global weighted estimates for the gradient of solutions to nonlinear elliptic equations (2013, methodology): “Since this procedure is similar to those made in the previous papers [5,10], we make a brief sketch for the completeness of the proof.”
• Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains (2012, methodology): “overcome the difficulty arising from the nonlinearity of the equation and the complexity of Reifenberg domains, we follow the ideas implemented in [6, 7 ] which make use of weak compactness, W 1, ∞ regularity of homogeneous equations, the Vitali covering lemma, and the Hardy‐Littlewood maximal funct”
• Nonlinear gradient estimates for elliptic equations of general type (2012, background): “This procedure makes a complete proof to be relatively technical and delicate (see, for instance, [2,4,8]).”