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Attention-based hybrid solvers for linear equations that are geometry aware Open
We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust precondit…
Fourth-Order Accurate Compact Scheme for First-Order Maxwell’s Equations Open
We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell’s equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-…
View article: Optimal Hardy‐weights for elliptic operators with mixed boundary conditions
Optimal Hardy‐weights for elliptic operators with mixed boundary conditions Open
We construct families of optimal Hardy‐weights for a subcritical linear second‐order elliptic operator with degenerate mixed boundary conditions. By an optimal Hardy‐weight for a subcritical operator we mean a nonzero nonnegative weight fu…
Fourth order accurate compact scheme for first-order maxwell's equations Open
We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-…
Optimal Hardy-weights for the (<i>p</i>, <i>A</i>)-Laplacian with a potential term Open
We construct new optimal $L^{p}$ Hardy-type inequalities for elliptic Schrödinger-type operators with a potential term.
Optimal Hardy-weights for the $(p,A)$-Laplacian with a potential term Open
We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schrödinger-type operators
View article: Optimal Hardy-weights for elliptic operators with mixed boundary conditions
Optimal Hardy-weights for elliptic operators with mixed boundary conditions Open
We construct families of optimal Hardy-weights for a subcritical linear second-order elliptic operator $(P,B)$ with degenerate mixed boundary conditions. By an optimal Hardy-weight for a subcritical operator we mean a nonzero nonnegative w…
View article: On criticality theory for elliptic mixed boundary value problems in divergence form
On criticality theory for elliptic mixed boundary value problems in divergence form Open
The paper is devoted to the study of positive solutions of a second-order linear elliptic equation in divergence form in a domain $D\subseteq \mathbb{R}^n$ that satisfy an oblique boundary condition on a portion of $\partial D$. First, we …