Abstract
We study existence and regularity of positive solutions of problems like
depending on the values of q > 0, 0 < θ < 1, and on the summability of the datum f ≥ 0 in Lebesgue spaces.
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D. Arcoya, P.J. Martínez-Aparicio, Quasilinear equations with natural growth. Rev. Mat. Iberoam., 24 (2008), 597–616.
D. Arcoya, S. Barile, P.J. Martínez-Aparicio, Singular quasilinear equations with quadratic growth in the gradient without sign condition. J. Math. Anal. Appl., 350 (2009), 401–408.
D. Arcoya, J. Carmona, T. Leonori, P.J. Martínez-Aparicio, L. Orsina, F. Petitta, Existence and nonexistence of solutions for singular quadratic quasilinear equations. J. Differential Equations, 249 (2009), 4006–4042.
L. Boccardo, Some nonlinear Dirichlet problems in L 1 involving lower order terms in divergence form. Progress in elliptic and parabolic partial differential equations (Capri, 1994), 43–57, Pitman Res. Notes Math. Ser. 350, Longman, Harlow, 1996.
Boccardo L.: A contribution to the theory of quasilinear elliptic equations and application to the minimization of integral functionals. Milan J. Math., 79, 193–206 (2011)
Boccardo L.: Dirichlet problems with singular and quadratic gradient lower order terms. ESAIM Control Optim. Calc. Var., 14, 411–426 (2008)
Boccardo L., Gallouët T.: Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations 17, 641–655 (1992)
L. Boccardo, T. Gallouët, Strongly nonlinear elliptic equations having natural growth terms and L 1 data. Nonlinear Anal., 19 (1992), 573–579.
Boccardo L., Gallouët T., Orsina L.: Existence and nonexistence of solutions for some nonlinear elliptic equations. J. Anal. Math., 73, 203–223 (1997)
L. Boccardo, F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Anal., 19 (1992), 581–597.
L. Boccardo, F. Murat, J.-P. Puel, Existence de solutions non bornées pour certaines équations quasi-linéaires. Portugaliae Math., 41 (1982), 507–534.
Boccardo L., Murat F., Puel J.-P.: L ∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result. SIAM J. Math. Anal., 23, 326–333 (1992)
E. De Giorgi, Semicontinuity theorems in the calculus of variations. Quaderni dell’Accademia Pontaniana, 56, Accademia Pontaniana, Naples, 2008.
D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order. Second edition. Grundlehren der Mathematischen Wissenschaften, 224, Springer-Verlag, Berlin, 1983.
Moreno-Mérida L.: A quasilinear Dirichlet problem with quadratic growth respect to the gradient and L1 data. Nonlinear Anal. 95, 450–459 (2014)
G. Stampacchia, Le probléme de Dirichlet pour les équations elliptiques du seconde ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble), 15 (1965), 189–258.
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Dedicato a David Arcoya (maestro di tutti noi) per i suoi cinquant’anni
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Boccardo, L., Moreno-Mérida, L. & Orsina, L. A Class of Quasilinear Dirichlet Problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms. Milan J. Math. 83, 157–176 (2015). https://doi.org/10.1007/s00032-015-0232-3
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DOI: https://doi.org/10.1007/s00032-015-0232-3