Gradient bounds for a widely degenerate orthotropic parabolic equation
Abstract
Abstract In this paper, we consider the following nonlinear parabolic equation $$ \partial _{t}u\,=\,\sum _{i=1}^{n}\partial _{x_{i}}\left[ (\vert u_{x_{i}}\vert -\delta _{i})_{+}^{p-1}\frac{u_{x_{i}}}{\vert u_{x_{i}}\vert }\right] \,\,\,\,\,\,\,\,\,\,\textrm{in}\,\,\,\Omega \times I, $$ ∂ t u = ∑ i = 1 n ∂ x i ( | u x i | - δ i ) + p - 1 u x i | u x i | in Ω × I , where $$\Omega $$ Ω is a bounded open subset of $$\mathbb {R}^{n}$$ R n for $$n\ge 2$$ n ≥ 2 , $$I\subset \mathbb {R}$$ I ⊂ R is a bounded open interval, $$p\ge 2$$ p ≥ 2 , $$\delta _{1},\ldots ,\delta _{n}$$ δ 1 , … , δ n are non-negative numbers and $$\left( \,\cdot \,\right) _{+}$$ · +
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Numerical methods in inverse problems
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 4
- Publication date
- 30 June 2026
- Language
- EN