Search results for "p-poisson problem"
showing 2 items of 2 documents
C1,α regularity for the normalized p-Poisson problem
2017
We consider the normalized p -Poisson problem − Δ N p u = f in Ω ⊂ R n . The normalized p -Laplacian Δ N p u := | Du | 2 − p Δ p u is in non-divergence form and arises for example from stochastic games. We prove C 1 ,α loc regularity with nearly optimal α for viscosity solutions of this problem. In the case f ∈ L ∞ ∩ C and p> 1 we use methods both from viscosity and weak theory, whereas in the case f ∈ L q ∩ C , q> max( n, p 2 , 2), and p> 2 we rely on the tools of nonlinear potential theory peerReviewed
$C^{1,��}$ regularity for the normalized $p$-Poisson problem
2017
We consider the normalized $p$-Poisson problem $$-��^N_p u=f \qquad \text{in}\quad ��.$$ The normalized $p$-Laplacian $��_p^{N}u:=|D u|^{2-p}��_p u$ is in non-divergence form and arises for example from stochastic games. We prove $C^{1,��}_{loc}$ regularity with nearly optimal $��$ for viscosity solutions of this problem. In the case $f\in L^{\infty}\cap C$ and $p>1$ we use methods both from viscosity and weak theory, whereas in the case $f\in L^q\cap C$, $q>\max(n,\frac p2,2)$, and $p>2$ we rely on the tools of nonlinear potential theory.