Solvability of quasilinear elliptic equations with strong dependence on the gradient
Copyright policy )Solvability of quasilinear elliptic equations with strong dependence on the gradient
We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving p‐Laplacian in the ball. We allow simultaneous strong dependence of the right‐hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro‐differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem. We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.
45J05, elliptic equation, radially symmetric, singular ordinary integro-differential equation, \(p\)-Laplace operator, decreasing, Nonlinear elliptic equations, elliptic equation; radially symmetric; strong dependence on the gradient, 35J60, a posteriori regularity, Integro-ordinary differential equations, strong dependence on the gradient, weak and strong solutions, QA1-939, spherically symmetric, Local existence and uniqueness theorems (PDE), Mathematics
45J05, elliptic equation, radially symmetric, singular ordinary integro-differential equation, \(p\)-Laplace operator, decreasing, Nonlinear elliptic equations, elliptic equation; radially symmetric; strong dependence on the gradient, 35J60, a posteriori regularity, Integro-ordinary differential equations, strong dependence on the gradient, weak and strong solutions, QA1-939, spherically symmetric, Local existence and uniqueness theorems (PDE), Mathematics
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