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We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like $$\left\{ \begin{aligned} &-{\rm div}\Big((a(x)+|u|^q) \nabla u\Big)= \frac{f}{|u|^\gamma}\ \ {\rm in}\ \Omega,\\ & u=0\ \ {\rm on}\ {\partial \Omega},\\ \end{aligned} \right.$$ where $\Omega$ is a bounded open subset of $\mathbb{R^N} (N \geq 2)$, $a(x)$ is a measurable nonnegative function, $q, \gamma> 0$ and the source $f$ is a nonnegative (not identicaly zero) function belonging to $L^m(\Omega)$ for some $m \geq 1$. Our results will depend on the summability of $f$ and on the values of $q, \gamma> 0$.
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참고문헌 (18)
참고문헌 신청
Lucio Boccardo / 2011 / A Contribution to the Theory of Quasilinear Elliptic Equations and Application to the Minimization of Integral Functionals / Milan Journal of Mathematics 79(1):193~206
Lucio Boccardo / 2015 / A Class of Quasilinear Dirichlet Problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms / Milan Journal of Mathematics 83(1):157~176
Lucio Boccardo / 1992 / Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations / Nonlinear Analysis: Theory, Methods & Applications 19(6):581~597
Lucio Boccardo / 2010 / Semilinear elliptic equations with singular nonlinearities / Calculus of Variations and Partial Differential Equations 37(3-4):363~380
José Carmona / 2016 / A Singular Semilinear Elliptic Equation with a Variable Exponent / Advanced Nonlinear Studies 16(3):491~498
Lucio Boccardo / 2015 / A Class of Quasilinear Dirichlet Problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms / Milan Journal of Mathematics 83(1):157~176
Lucio Boccardo / 1992 / Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations / Nonlinear Analysis: Theory, Methods & Applications 19(6):581~597
Lucio Boccardo / 2010 / Semilinear elliptic equations with singular nonlinearities / Calculus of Variations and Partial Differential Equations 37(3-4):363~380
José Carmona / 2016 / A Singular Semilinear Elliptic Equation with a Variable Exponent / Advanced Nonlinear Studies 16(3):491~498
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