Related papers: Partial regularity for $BV^\mathcal{B}$ minimizers
In this paper, we establish a $C^{1,\alpha}$-regularity theorem for almost-minimizers of the functional $\mathcal{F}_{\varepsilon,\gamma}=P-\gamma P_{\varepsilon}$, where $\gamma\in(0,1)$ and $P_{\varepsilon}$ is a nonlocal energy…
We consider the operators \[ \nabla_X\cdot(A(X)\nabla_X),\ \nabla_X\cdot(A(X)\nabla_X)-\partial_t,\ \nabla_X\cdot(A(X)\nabla_X)+X\cdot\nabla_Y-\partial_t, \] where $X\in \Omega$, $(X,t)\in \Omega\times \mathbb R$ and $(X,Y,t)\in…
In this paper we study the regularity of the local minima of integral functionals: in particular, not convexity (quasi-convexity, policonvexity or rank one convexity) hypothesis will be made on the density, neither structure hypothesis nor…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of…
We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(\lambda_+(x)|\mathbf{u}^+|^{q+1}+\lambda_-(x)|\mathbf{u}^-|^{q+1}\right)\right)dx,\quad0<q<1.$$ For H\"older continuous…
We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the…
We prove the existence of minimizers for some constrained variational problems on $BV(\Omega)$, under subcritical and critical restrictions, involving the affine energy introduced by Zhang in \cite{Z}. Related functionals have non-coercive…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
We prove some variational analysis of regularity and weak convergence of nonlocal variational principle.
This paper is concerned with the regularity of shape optimizers of a class of isoperimetric problems under convexity constraint. We prove that minimizers of the sum of the perimeter and a perturbative term, among convex shapes, are C…
We study the homogenization problem for matrix strongly elliptic operators on $L_2(\mathbb R^d)^n$ of the form $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$. The function $A$ is Lipschitz in the first variable and…
The maximal B_{p,q}^{s}-regularity properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal ell{\i}p{\i}t{\i}c equation in B_{p,q}^{s} is sectorial and also is…
We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restriction on the…
We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $\mathrm{C}^{1,\alpha}$ or $\mathrm{C}^{\infty}$-partial regularity. Different from previous contributions, the method is…
The paper makes use of recent results in the theory of Banach lattices and positive operators to deal with abstract semilinear equations. The aim is to work with minimal or no regularity conditions on the boundary of the domains, where the…
S.G.Krein's conjecture concerning Birkhoff-regularity of dissipative differential operators has been proved in the even order case. As a byproduct an existence of the limit of characteristic matrix as in the lower half-plane has been…
We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(|u|)\nabla u)=f &\text{in }\Omega,\\[.2cm] \displaystyle\frac{\partial…