Local boundedness for weak solutions to strongly degenerate orthotropic parabolic equations
Year: 2025
Type: article
Abstract: We prove the local boundedness of local weak solutions to the parabolic equation $$ \partial _{t}u\,=\,\sum _{i=1}^{n}\partial _{x_{i}}\left[ (\vert u_{x_{i}}\vert -\delta _{i})_{+}^{p-1}\frac{u_{x_{i}}}{\vert u_{x_{i}}\vert }\right] \,\,\,\,\,\,\,\,\,\,\textrm{in}\,\,\,\Omega _{T}=\Omega \times (0,T]\,, $$ ∂ t u = ∑ i = 1 n ∂ x i ( | u x i | - δ i ) + p - 1 u x i | u x i | in Ω T = Ω × ( 0 , T ] , where $$\Omega $$ Ω is a bounded domain in $${\mathbb {R}}^{n}$$ R n with $$n\ge 2$$ n ≥ 2 , $$p\ge 2$$ p ≥ 2 , $$\delta _{1},\ldots ,\delta _{n}$$ δ 1 , … , δ n are non-negative numbers and $$\left( \,\cdot \,\right) _{+}$$ · + denotes the positive part. The main novelty here is that the
Source: Ricerche di Matematica
Authors: Pasquale Ambrosio, Simone Ciani
Institution: University of Bologna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4416410768