Geodesic
Boundedness of the weak solutions to conormal problems for quasilinear elliptic equations with Morrey data
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 7-25

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We consider a conormal problem for a class of quasilinear divergence form elliptic equations modeled on the $m$-Laplacian. The nonlinearities support controlled growths in the solution and its gradient, while their behaviour with respect to the independent variable is restrained in terms of Morrey spaces. We show global essential boundedness for the weak solutions, generalizing this way the classical $L^p$-result of Ladyzhenskaya and Ural'tseva to the settings of the Morrey spaces. 
@article{ZNSL_2024_536_a1,
     author = {E. A. Alfano and L. Fattorusso and D. K. Palagachev and L. G. Softova},
     title = {Boundedness of the weak solutions to conormal problems for quasilinear elliptic equations with {Morrey} data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--25},
     publisher = {mathdoc},
     volume = {536},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a1/}
}
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E. A. Alfano; L. Fattorusso; D. K. Palagachev; L. G. Softova. Boundedness of the weak solutions to conormal problems for quasilinear elliptic equations with Morrey data. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 7-25. http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a1/