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arXiv · 2206.06707

Large solutions of degenerate and/or singular quasilinear elliptic equations in a ball

Raj Narayan Dhara
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Abstract

We consider local weak large solutions with its blow-up rate near the boundary to certain class of degenerate and/or singular quasilinear elliptic equation\\ ${\rm div}(d^{\alpha}(x,\partial{}B)\Phi_p(\nabla u)) = b(x)f(u)$ in a ball B, where $f$ is normalized regularly varying at infinity with index $\sigma+1>p-1,\ p>1$. In particular, how the asymptotic behavior of the solution changes over the varying index and degeneracy and/ or singularity present in the equation. We also include the second order blow-up rate for the corresponding semilinear problem.

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Raj Narayan Dhara. 2022-06-14. Large solutions of degenerate and/or singular quasilinear elliptic equations in a ball. https://arxiv.org/abs/2206.06707

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