Regularity theory for a class of quasilinear equations |
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| Authors: | L H de Miranda M Montenegro |
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| Institution: | 1. Universidade de Brasília, Departamento de Matemática, Campus Universitário Darcy Ribeiro, ICC Centro, Bloco A, Asa Norte, Brasília‐DF, Brazil;2. Universidade Estadual de Campinas, IMECC‐Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, Campinas‐SP, Brazil |
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| Abstract: | This paper addresses the analysis of the weak solution of  in a bounded domain Ω subject to the boundary condition  on  , when the data f belongs to  and  . We prove existence and uniqueness of solution for this problem in the Nikolskii space  . Moreover, we obtain energy estimates regarding the Nikolskii norm of ω in terms of the  norm of f. |
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| Keywords: | p‐Laplacian regularity theory Nikolskii spaces 35B65 35J92 46E35 |
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