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Asymptotic behaviour of principal eigenfunctions and large deviations

Dear Math Overflowers, I am currently interested in a particular problem involving Large Deviations. I am only going to talk about the PDE side of the problem, but I'll be happy to provide more ...
leo monsaingeon's user avatar
3 votes
0 answers
140 views

Sufficient condition for the unique solvability of Dirichlet problem of Hamilton-Jacobi equation

It shall be an old story in PDE. I am looking for a sufficient condition of Dirichlet problem for the existence of the unique viscosity solution of the equation in the form of $$\inf_{a \in [-1,1]} \{...
kenneth's user avatar
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2 votes
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52 views

Reference Request: Dirichlet operators with singular coefficients

Let $d\geq 2$, $\delta \in (0,1)$ and let $\mathcal{L}_{d,\delta}$ be the second order differential operator defined by \begin{align*} \mathcal{L}_{d,\delta}(f)(x) = \Delta(f)(x)-\delta \|x\|^{\delta-...
user69642's user avatar
  • 778
1 vote
0 answers
152 views

Poisson Kernel and solution formula for fractional elliptic problem

$$ k (-\Delta)^s u + u = 0, \qquad x \in U, \\ u(x) = f(x), \qquad x \in \mathbb R^n \setminus U, $$ with $f \in L^\infty(\mathbb R^n)$, $k>0$, and $(-\Delta)^s$ is the singular integral ...
Riku's user avatar
  • 839
1 vote
0 answers
358 views

"Brownian motion" related to the $p$-Laplace operator

The link between the Brownian motion and the Laplace operator is well-known. What stochastic process plays an analogous role with respect to the $p$-Laplace operator?
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34 views

Inequalities for generalized variance

Let $(X, \mu)$ be a measured space with $\mu(X) = 1$. Given $\phi \in L^\infty(X, \mu)$, $\phi > 0$, let me define, for $\alpha \geq 1$, $\beta > 0$, the quantity $$ I(\alpha, \beta) = \left(\...
Romain Gicquaud's user avatar