Regularizing Effects for a Singular Elliptic Problem - Ida de Bonis; Maria Michaela Porzio (Axioms)
In this paper, we prove existence and regularity results for a nonlinear elliptic problem of p-Laplacian type with a singular potential like <semantics><mstyle scriptlevel="0" displaystyle="true">fuγ</mstyle></semantics> and a lower order term <semantics>bu</semantics>, where u is the solution and b and f are only assumed to be summable functions. We show that, despite the lack of regularity of the data, for suitable choices of the function b in the lower order term, a strong regularizing effect appears. In particular we exhibit the existence of bounded solutions. Worth notice is that this result fails if <semantics>b≡0</semantics>, i.e., in absence of the lower order term. Moreover, we show that, if the singularity is “not too large” (i.e., <semantics>γ≤1</semantics>), such a regular solution is also unique.