Revised regularity results for quasilinear elliptic problems driven by the $$\Phi $$Φ-Laplacian operator

2019 ◽  
Vol 161 (3-4) ◽  
pp. 563-582
Author(s):  
E. D. Silva ◽  
M. L. Carvalho ◽  
J. C. de Albuquerque
Keyword(s):  
Elliptic Problems ◽  
Laplacian Operator ◽  
Quasilinear Elliptic Problems ◽  
Regularity Results ◽  
Quasilinear Elliptic

scholarly journals Anisotropic 1-Laplacian problems with unbounded weights

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
Juan C. Ortiz Chata ◽  
Marcos T. O. Pimenta ◽  
Sergio Segura de León
Keyword(s):  
Bounded Variation ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Weighted Spaces ◽  
Laplacian Operator ◽  
Functions Of Bounded Variation ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractIn this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg’s inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting.

Quasilinear elliptic problems with singular and homogeneous lower order terms

2019 ◽  
Vol 179 ◽  
pp. 105-130 ◽  
Author(s):  
José Carmona ◽  
Tommaso Leonori ◽  
Salvador López-Martínez ◽  
Pedro J. Martínez-Aparicio
Keyword(s):  
Lower Order ◽  
Elliptic Problems ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic ◽  
Lower Order Terms
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