Questions tagged [p-laplace]

Questions involving the $p$-Laplace operator $\Delta_p u=\operatorname{div}(|\nabla u|^{p-2}\nabla u)$.

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Euler-Lagrange equations for $p$-Harmonic vector fields

Harmonic vector fields are critical points of Dirichlet energy function on the set of all unit vector fields on $M$, which is defined as follows: $$E(X):=\frac{1}{2}\int_M\|dX\|^2\mathrm{dVol_g}\qquad ...
C.F.G's user avatar
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2 votes
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Density of restrictions of $p$-harmonic functions on a hypersurface

Let $\omega,\Omega\subset\mathbb R^n$, $n\geq2$, be bounded smooth domains so that $\bar\omega\subset\Omega$. Let $1<p<\infty$. Define the boundary space $B=W^{1,p}(\omega)/W^{1,p}_0(\omega)$; ...
Joonas Ilmavirta's user avatar
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206 views

3D Homogenous Laplace equation with integral boundary conditions

I have the 3D Laplace equation: $$\nabla^{2} T_w = 0$$ where $\nabla^{2}=(\frac{\partial^{2}}{\partial x^2}+\frac{\partial^{2}}{\partial y^2}+\frac{\partial^{2}}{\partial z^2})$ defined on $x \in [0,...
Avrana's user avatar
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