4 papers · 1 filter
Gradient regularity for -harmonic functions
Verena Bögelein, Frank Duzaar, Naian Liao +2
We study the local regularity properties of -harmonic functions, i.e. local weak solutions to the fractional -Laplace equation of order in the case $p\in (1,…
Mountain Pass Solutions for an entire semipositone problem involving the Grushin Subelliptic Operator
Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi
For we study the following semipositone problem where is the Grushin operator $$ Δ_ γu(z) = Δ_x u(z) + \ver…
Regularity for the fractional -Laplace equation
Verena Bögelein, Frank Duzaar, Naian Liao +2
Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional -Laplace equation of order in the case . Depending on the regime considere…
A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results
Giovanni Molica Bisci, Paolo Malanchini, Simone Secchi
We consider the boundary value problem $$ \cases{ -Δ_γu = λu + \left\vert u \right\vert^{2^*_γ-2}u &in $Ω$\cr u = 0 &on $\partialΩ$,\cr } $$ where is an open bounded domain in…