Removable sets for Hölder continuous solutions of quasilinear elliptic equations with lower order terms

2012 ◽  
Vol 356 (1) ◽  
pp. 355-372 ◽  
Author(s):  
Takayori Ono
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Removable Sets ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

scholarly journals On Carlson's Type Removability Test for the Degenerate Quasilinear Elliptic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
Farman I. Mamedov ◽  
Aslan D. Quliyev ◽  
Mirfaig M. Mirheydarli
Keyword(s):  
Hausdorff Measure ◽  
Elliptic Equations ◽  
Type Theorem ◽  
Quasilinear Elliptic Equations ◽  
Compact Set ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Muckenhoupt Class ◽  
Removable Sets ◽  
Quasilinear Elliptic

Carlson's type theorem on removable sets forα-Holder continuous solutions is investigated for the quasilinear elliptic equationsdiv A(x,u,∇u)=0,having degenerationωin the Muckenhoupt class. In partial, whenαis sufficiently small and the operator is weightedp-Laplacian, we show that the compact setEis removable if and only if the Hausdorff measureΛω−p+(p−1)α(E)=0.

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

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