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We establish existence and pointwise estimates of fundamental solutions and Greens matrices for divergence form, second order strongly elliptic systems in a domain $Omega subseteq mathbb{R}^n$, $n geq 3$, under the assumption that solutions of the system satisfy De Giorgi-Nash type local H{o}lder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-textrm{div} (a(x) abla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of $Omega$ wher
Under various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving Holder semi-norms not with respect to all, but only with respect to some of the independent
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a conjecture by Ga
We establish existence and various estimates of fundamental matrices and Greens matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems satisfy an inter
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption which calle