Geodesic
A note on Campanato's $L^p$-regularity with continuous coefficients
Eurasian mathematical journal, Tome 13 (2022) no. 4, pp. 44-53

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In this note we consider local weak solutions of elliptic equations in variational form with data in $L^p$. We refine the classical approach due to Campanato and Stampacchia and we prove the $L^p$-regularity for the solutions assuming the coefficients merely continuous. This result shows that it is possible to prove the same sharp $L^p$-regularity results that can be proved using classical singular kernel approach also with the variational regularity approach introduced by De Giorgi. This method works for general operators: parabolic, in nonvariational form, of order $2m$. 
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     author = {C. Bernardini and V. Vespri and M. Zaccaron},
     title = {A note on {Campanato's} $L^p$-regularity with continuous coefficients},
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     url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_4_a2/}
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C. Bernardini; V. Vespri; M. Zaccaron. A note on Campanato's $L^p$-regularity with continuous coefficients. Eurasian mathematical journal, Tome 13 (2022) no. 4, pp. 44-53. http://geodesic.mathdoc.fr/item/EMJ_2022_13_4_a2/