The weak solutions of the p-harmonic equation are, by definition, members of the Sobolev space. In fact, they are also of class. More precisely, a weak solution can be redefined in a set of Lebesgue measure zero, so that the new function is locally Hölder continuous with exponent.
CITATION STYLE
Lindqvist, P. (2019). Regularity Theory. In SpringerBriefs in Mathematics (pp. 17–28). Springer Science and Business Media B.V. https://doi.org/10.1007/978-3-030-14501-9_3
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