On some partial differential inequalities with gradient terms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 40-48

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Using a modification of the nonlinear capacity method, we obtain necessary conditions for the solvability of some nonlinear partial differential equations and inequalities containing the polyharmonic operator and terms that depend on the norm of the gradient of the solution, both in the entire space and in bounded domains; in the latter case the coefficients of the inequality are allowed to have singularities.
@article{TM_2013_283_a3,
     author = {E. I. Galakhov},
     title = {On some partial differential inequalities with gradient terms},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {40--48},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_283_a3/}
}
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E. I. Galakhov. On some partial differential inequalities with gradient terms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 40-48. http://geodesic.mathdoc.fr/item/TM_2013_283_a3/