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- Title
A DIRECT PROOF OF EXISTENCE OF WEAK SOLUTIONS TO ELLIPTIC PROBLEMS.
- Authors
CHLEBICKA, IWONA; KARPPINEN, ARTTU; YING LI
- Abstract
We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower-order terms. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak--Orlicz spaces generated by an N-function M:Ω x ℝd → [0, ∞). Neither ∇2 nor Δ2 conditions are imposed on M. Our results cover among others problems with anisotropic polynomial, Orlicz, variable exponent, and double phase growth.
- Subjects
ORLICZ spaces; ELLIPTIC equations; NONLINEAR equations; PARTIAL differential equations; BOUNDARY value problems
- Publication
Topological Methods in Nonlinear Analysis, 2023, Vol 62, Issue 2, p643
- ISSN
1230-3429
- Publication type
Article
- DOI
10.12775/TMNA.2023.019