The Calderón-Zygmund property for quasilinear divergence form equations over Reifenberg flat domains |
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Authors: | Dian K Palagachev Lubomira G Softova |
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Institution: | a Politecnico di Bari, Dipartimento di Matematica, Via E. Orabona, 4, 70 125 Bari, Italyb Seconda Università di Napoli, Dipartimento di Ingegneria Civile, Via Roma, 29, 81 031 Aversa, Italy |
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Abstract: | The results by Palagachev (2009) 3] regarding global Hölder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient. Moreover, the principal coefficients are discontinuous with discontinuity measured in terms of small BMO norms and the underlying domain is supposed to have fractal boundary satisfying a condition of Reifenberg flatness. The results are extended to the case of parabolic operators as well. |
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Keywords: | primary 35J62 secondary 35R05 35B65 35K59 |
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