engleski

Generating singularities of quasilinear elliptic equations

Let $1<p<N$. If the right-hand side of a quasilinear p-Laplace equation has singularity of order $\gamma\in(p, 1+N/p')$ at a point $x_0\in\Omega$, then each supersolution which is essentially bounded from below on a neighborhood of $x_0$, has singularity of order $\frac{;\gamma-p};{;p-1};$ at $x_0$. Moreover, we obtain an explicit and sharp lower bound on the supersolution in the neighborhood of $x_0$.

quasilinear elliptic; p-Laplacian; singularity

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