TY - JOUR
T1 - WEIGHTED ANISOTROPIC SOBOLEV INEQUALITY WITH EXTREMAL AND ASSOCIATED SINGULAR PROBLEMS
AU - Bal, Kaushik
AU - Garain, Prashanta
N1 - Funding Information:
We are thankful to the anonymous reviewer for the fruitful comments and suggestions that greatly improved the previous version of the manuscript. Research work of first author is funded by Matrics grant MTR/2020/000594. The second author thanks Ben Gurion University of the Negev, Israel and Uppsala University, Sweden for the nice hospitality.
Publisher Copyright:
© 2023 Differential and Integral Equation. All rights reserved.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - We consider singular problems associated with the weighted anisotropic p-Laplace operator Hp, wu = div(w(x)(H(∇u))p-1∇H(∇u)), where H is a Finsler-Minkowski norm and the weight w belongs to a class of p-admissible weights, which may vanish or blow up near the origin. We discuss existence and regularity properties of weak solutions for the mixed and exponential singular nonlinearities. In particular, the existence result for the purely singular problem leads us to the validity of a weighted anisotropic Sobolev inequality with an extremal.
AB - We consider singular problems associated with the weighted anisotropic p-Laplace operator Hp, wu = div(w(x)(H(∇u))p-1∇H(∇u)), where H is a Finsler-Minkowski norm and the weight w belongs to a class of p-admissible weights, which may vanish or blow up near the origin. We discuss existence and regularity properties of weak solutions for the mixed and exponential singular nonlinearities. In particular, the existence result for the purely singular problem leads us to the validity of a weighted anisotropic Sobolev inequality with an extremal.
UR - http://www.scopus.com/inward/record.url?scp=85144488506&partnerID=8YFLogxK
U2 - 10.57262/die036-0102-59
DO - 10.57262/die036-0102-59
M3 - Article
AN - SCOPUS:85144488506
VL - 36
SP - 59
EP - 92
JO - Differential and Integral Equations
JF - Differential and Integral Equations
SN - 0893-4983
IS - 1-2
ER -