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math.AP2024★ 1 cited
Regularity results for a class of mixed local and nonlocal singular problems involving distance function
Kaushik Bal, Stuti Das
We investigate the following mixed local and nonlocal quasilinear equation with singularity given by \begin{eqnarray*} \begin{split} -Δ_pu+(-Δ)_q^s u&=\frac{f(x)}{u^δ}\text { in }…
math.AP2024
Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity
Kaushik Bal, Stuti Das
We will prove multiplicity results for the mixed local-nonlocal elliptic equation of the form \begin{eqnarray} \begin{split} -Δ_pu+(-Δ)_p^s u&=\fracλ{u^γ}+u^r \text { in } Ω, \\u&>…
math.AP2024
On a mixed local-nonlocal evolution equation with singular nonlinearity
Kaushik Bal, Stuti Das
We will prove several existence and regularity results for the mixed local-nonlocal parabolic equation of the form \begin{eqnarray} \begin{split} u_t-Δu+(-Δ)^s u&=\frac{f(x,t)}{u^{…