Elliptic Partial Differential Equations

282 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Linear theory for a mixed operator with Neumann conditions (2020, unknown): “We combine for this proof some classical and nonlocal techniques, see e.g. [34, 35,43,45,46,53,54].”
Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator (2012, background): “By elliptic regularity (see [11], for example), u L B1 ≤ CnM u L2 B2 , for M > 1.”
Gradient estimates for elliptic systems in non-smooth domains (2008, background): “4) for some positive constant C = C(c0, c1, n, N , ) provided that is a bounded open domain and the tensor coefficients are bounded and uniformly elliptic (See [9,13,15]).”
The Allen–Cahn equation on closed manifolds (2016, unknown): “19 of [31]) guarantee the existence of a positive constant C̃ = C̃(δ̃,W ) such that supB1/2(0)|∇ũ|≤ C̃.”
Liouville theorems for stable solutions of biharmonic problem (2013, unknown): “4 in [10]: For any p ∈ [2,∞), there exists (p) > 0 such that if ∆w + ρw = 0 in B2 with ‖ρ‖Ln2 (B2) ≤ (p), we have (2.”
Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations (2019, background): “For convenience of the reader we provide the arguments following the presentation in [20].”